G B 



Waier-Supply and Irrigation Paper No. 187 Series M, General Hydrographic Investigations, 19 






DEPARTMENT OF THE INTERIOR 

UNITED STATES GEOLOGICAL SURVEY 

CHARLES D. WALCOTT, Director 



DETERMINATION OF STREAM FLOW 
DURING THE FROZEN 



BY 



H. K. BARROWS and ROBERT E. HORTON 




WASHINGTON 

GOVERNMENT PRINTING OFFICE 
1907 




CIass^_J>L 
Book 



Digitized by the Internet Archive 
in 2011 with funding from 
The Library of Congress 



http://www.archive.org/details/determinationofsOObarr 






Water-Supply and Irrigation Paper No. 187 Series M, General Hydrographic Investigations, 19 

DEPARTMENT OF THE [NTERIOB 

UNITED STATES GEOLOGICAL SURVEY 

CHARLES D. WALCOTT, Director 






DETERMINATION OF STREAM FLOW 
DURING THE FROZEN 

SEASON 



H. K. BARROWS and ROBERT E. HORTON 




WASHINGTON 

GOVERNMENT PRINTING OFFICE 

19 07 



&^ 



V 

-p 



o- 



FEB 28 1907 
ft, dD, 



CONTENTS. 



Page. 

Importance of winter records of si ream How 5 

Methods of gaging streams during the open sen son 6 

General statement 6 

Weir method 6 

Velocity method 6 

Slope method 7 

( Conditions during the winter season 7 

Factors affecting ice formation 7 

Classification of winter conditions 8 

Duration of ice season 9 

Change in thickness of ice 10 

Surface, anchor, am! needle ice 10 

Range of winter gage heights 13 

Flow of str< ams under ice cover 14 

General considerations 14 

Friction due to air and ice 14 

Relative importance of air and ice friction 15 

Variation in slope due to freezing 17 

Change in area of waterway required by freezing 18 

Effecl of thickness of ice on flow . 19 

Methods of obtaining winter records 21 

Current-meter stations . _ 21 

Gage heights 21 

Current-meter discharge measurements 22 

Stat ions at dams 25 

Estimates from precipitation 25 

Winter records . . 26 

Conditions at stations 26 

Catskill Creek at South Cairo, N. Y 26 

Connecticut River at Orfonl , X . II 29 

Esopus Creek at Kingston, N. Y 30 

Fish River at Wallagrass, Me 32 

Kennebec River at North Anson, Me _ 33 

Rondout Creek at Rosendale, N. Y 34 

Wallkill River at Newpaltz, N. Y - 35 

Winooski River at Richmond , Vt — 37 

Gage heights and discharge measurements 38 

Station rating ourves for ice cover 43 

General considerations - 43 

Wallkill River at Newpaltz, X. Y - 43 

Kennebec River at North Anson, Me - 44 

Connecticut River at Orfonl, N. II 45 

3 



4 CONTENTS AND ILLUSTRATIONS. 

Winter records — Continued. 

Station rating curves for ice cover — Continued. 

General form of rating curve for ice cover 45 

Relation between discharge under ice cover and for open section 46 

Vertical velocity measurements under ice cover 46 

Details of vertical velocity curves 46 

Summaries of vertical velocity curves 72 

Form of vertical velocity curves 75 

Relation of depth and velocity to form of curve 77 

Comparison of vertical velocity curves with and without ice cover 78 

Position of threads of mean velocity 79 

Position of maximum velocity and relation to mean velocity 81 

Relation of velocity at mid depth to mean velocity. . _ 82 

Relation of mean of velocities at 0.2 and 0.8 depth to mean velocity 83 

Percentage variation in observations at different depths _ . 85 

Slope determinations and values of n in Kutter's formula, under ice conditions 87 

Data from other sources _ _ 88 

Conclusions 89 

Practicability of winter estimates of flow _ 89 

Recommendations as to methods _ _ 89 

Index 1 91 



ILLUSTRATIONS. 



Page. 
Plate I. A, Gaging station on Sandy River at Madison, Me-., at dam of Madison 

Electric Company; B, Gaging station on Winooski River at Richmond, Vt 24 

Fig. 1. Cross sections of Chemung River at Chemung, N. Y , showing effect of 

needle ice 12 

2. Effect of freezing on a smooth section of a river terminated by rapids . . 17 

3. Effect of change of stage on discharge under ice cover, with varying 

thickness of ice , 20 

4. Rating and velocity curves under ice cover, Wallkill River, New York . 43 

5. Rating curve under ice cover, Kennebec River, Maine 44 

6. Rating curve under ice cover, Connecticut River, New Hampshire 45 

7. Form of vertical velocity curves 75 

8. Comparison of vertical velocity curves for streams with and without ice 

cover 1 78 

9. Vertical velocity curves under ice cover, Kennebec River, Maine 79 

10. Vertical velocity curve under ice cover, Wallkill River, New York. 80 

11. Vertical velocity curves under ice cover, Connecticut River, New Hamp- 

shire , 81 

12. Vertical velocity curves under ice cover, Fish River, Maine 82 

13. Effect of depth on form of vertical velocity curves under ice 83 

14. Effect of very rough, broken, and tilted ice on form of vertical velocity 

curves under ice cover 84 



DETERMINATION OF STREAM FLOW 
I H T RING THE FROZEN SEASON. 



Bv II. K. Barrows and R. E. Horton. 



IMPORTANCE OF WINTER RECORDS OF STREAM FLOW. 

Estimates of the (low of rivers are now being made by the United 
States Geological Survey in all parts of the country. To a great 
extent these are based on daily gage readings and numerous current- 
meter measurements. 

In the northern and central parts of the United States the streams 
may be closed by a more or less permanent ice cover for a consider- 
able portion of the year. This period varies from nearly five months 
in the extreme north to a few weeks or less in the Central and Atlantic 
States. 

The methods in use for estimating flow under open-channel condi- 
tions have become well defined, and the limits of accuracy are known 
to be reasonable. On the other hand, the laws governing the flow 
of rivers that are frozen over have been but little investigated, and 
methods for estimating the flow under such conditions have not been 
formulated. Moreover, in winter the measurement of precipitation 
is more difficult, and available data of this kind are much less accurate 
than in summer. Finally, there is not even an approximate relation 
between the snowfall and the stream flow, so that the failure to obtain 
winter records of flow at a gaging station means a considerable per- 
centage of uncertainty as to the total run-off as well as to its distri- 
bution. 

In the Northern States droughts are apt to occur in the late sum- 
mer or fall and during the winter. At times this condition of drought 
may be nearly or quite continuous between these two periods, with 
its culmination in January or February. If there is no melting of 
snow during the winter, the inflow to streams that freeze is chiefly 
derived from springs, ground water, and lake storage, and in a long, 
cold winter, especially if it succeeds a period of low water, the mini- 
mum flow for the year may be reached and continue for some time. 
Estimates of flow, therefore, to be of conclusive value on streams 
utilized for water power, must embrace these winter periods of low 
water. 

5 



6 STREAM FLOW DURING THE FROZEN SEASON. 

METHODS OF GAGING STREAMS DURING THE OPEN 

SEASON. 

GENERAL STATEMENT. 

The methods of stream gaging in common use by the United States 
Geological Survey contemplate especially the determination of dis- 
charge when streams are free from ice at or near the gaging stations. 
One object of the present paper is to determine what modifications 
of these methods are necessary to secure good results when the streams 
are ice covered. With this in view a brief description of open-water 
methods is given below. 

In general a record of the fluctuations in stage is obtained by daily 
reading a gage or gages. Various methods are used to obtain a rat- 
ing of the stream so that the discharge in second-feet can be determined 
from the gage readings. Three principal methods of rating are in 
use — (1) the weir method, in which a weir or dam is used and the flow 
is computed for a given gage height; (2) the velocity method, in 
which a series of current-meter or float gagings are made at a given 
cross section and a discharge rating curve is obtained for that cross 
section; (3) the slope method, in which observations are made of the 
mean cross section and surface slope in a stretch of the river, and the 
velocity is computed by the Chezy-Kutter formula, V = C\/RS, a 
suitable value being assumed for the coefficient C. 

WEIR METHOD. 

Weirs of standard type with sharp crest can be used on small 
streams only, on account of the cost of installation and liability to 
injury. Where practicable, they offer the best facilities for deter- 
mining the flow. . The flow at dam stations is usually divided — part 
going over the dam, part through the wheels, and part through by- 
channels. A weir formula with modified coefficient is used to com- 
pute the flow over the dam. The wheels are used as meters, a record 
being kept of gate openings, head, etc. Flow through by-channels 
which at many dams occurs only at intervals, is computed by the use 
of weirs, orifices, etc. The sum of these components is the total 
discharge of the river at the section. The general methods used at 
stations of this character are fully described in Water-Supply Paper 
No. 150. 

VELOCITY METHOD. 

The determination of the rate of flow past a certain section of a 
stream at a given time is termed a "discharge measurement." This 
rate is the product of two factors — the mean velocity and the area of 
cross section. The mean velocity is a function of surface slope, 
wetted perimeter, roughness of bed, and the channel conditions at, 
above, and below the gage section. In this method it is assumed 



WINTER CONDITIONS. 7 

thai ilif stream bed is constant in form and position and thai the 
mean velocity at any given stage will always be the same There- 
fore a rating curve may be obtained by plotting the results of a suffi- 
cient number of discharge measurements at differenl stages. In 
making the measurements an arbitrary number of points, known as 
"measuring points," arc laid off on a line perpendicular to the thread 
of the stream, and the velocity and depth are observed. These 
points art 1 usually at regular intervals from 2 to '_'<) feet apart, depend- 
ing on the si/.e and condition of the stream. The current meter is 
commonly used for obtaining velocities, although in a few cases rod or 
tube floats are utilized for this purpose. The area is thus divided 
into small sections in which the velocity is observed and the discharge 
computed, and the sum of the values for these sections gives the total 
area and discharge. If a sufficient number of discharge measure- 
ments are made at different stages, a rating table can be constructed 
that will show the discharge at any stage of the stream. The methods 
used in selecting current-meter stations and in collecting data are 
fully described in Water-Supply Papers Nos. 94 and 95. 

SLOPE METHOD. 

The results obtained from the slope method are in general only 
roughly approximate, owing to the difficulty in obtaining accurate 
data and the uncertainty of the value to be used for n in Kutter's 
formula. The most common use of this method is in estimating flood 
discharge of streams when the only data available are the cross sec- 
tions, the surface slope as shown by marks along the bank, and a 
knowledge of the general conditions. 

Throughout this paper velocities are expressed in feet per second, 
gage heights in feet, and the volume of flow of streams in cubic feet 
per second, or second-feet. 

CONDITIONS DURING THE WINTER SEASON". 

FACTORS AFFECTING ICE FORMATION. 

Rarely, if ever, in this country does a stream of any size freeze over 
throughout its whole length, there being usually short stretches that 
remain more or less open. Two important factors govern the forma- 
tion of ice on streams — (1) the climatic or general temperature con- 
ditions; (2) the size and character of the stream and the conditions 
affecting its flow. 

In California, Washington, and Oregon, and south of latitude 37°, 
with the exception of perhaps a portion of northern New Mexico and 
Arizona in the Rocky Mountain district, the rivers do not in general 
freeze over sufficiently to affect records of flow or to occasion any 
change in methods from those of the open season. 



8 STREAM FLOW DURING THE FROZEN SEASON. 

In the most general sense, the character of the bed and banks of a 
stream depends on its slope and the materials' over which it flows. 
A stream will not freeze over unless the water has a temperature as 
low as 32° F. and is comparatively still. If the water is greatly agi- 
tated, needle ice will be formed instead of an ice cover. This ten- 
dency to form needle ice always exists at rapids, particularly if the 
stream bed is very rough. If the cold is extreme and long continued 
even such places may eventually become frozen — the freezing start- 
ing at the water's edge or around rocks and piers, where the velocity 
is lower, and extending toward the center of the stream. The result, 
however, is not in any case a smooth ice cover, but a piling up of very 
rough or " honeycombed " ice which may be partly supported by rocks. 

Where dams have been constructed there is-usually above the dam 
more or less pondage and a great diminution in velocity, so that such 
portions of a river freeze over very readily. Below the dam quick 
water is frequently left, and conditions may be. the same as at rapids. 

Any special conditions tending to raise the temperature of the water 
may have a marked effect on the time or manner of freezing over of a 
portion of a stream. Near the outlets of lakes or in streams fed by 
springs or ground water there may be a sufficient inflow of water 
having a temperature considerably above 32° F. to prevent wholly or 
r.t least for some time the formation of an ice cover. Such condi- 
tions are also potent in assisting the rapid wearing away of the under 
surface of the ice and, in general, they result in very unstable condi- 
tions as regards ice cover. The temperature of springs is ordinarily 
about equal to the average annual temperature of the locality, which 
is for the Northern States 40° to 50° F. 

CLASSIFICATION OF WINTER CONDITIONS. 

It is evident that streams of any considerable length can not be 
classified as a whole with regard to ice formation or winter condi- 
tions, for the reason that very diverse conditions may occur at differ- 
ent parts of the same stream. The conditions on short stretches of 
streams, and particularly on such stretches as need to be considered 
in selecting current-meter stations, may be classified as fellows : 

Classification of winter conditions at current-meter stations. 

(1) Smooth, permanent ice cover. 

(2) Tendency for anchor or needle ice to accumulate underneath ice cover. 

(3) Unstable ice cover, due to — 

(a) Effect of warmer inflow from lakes or tributary streams. 
(&) Effect of inflow of ground water. 

( c) Effect of warm currents due to artificial causes, such as factory waste, etc. 

(d) Concentrated quick water and wearing away due to friction. 

(e) Considerable fluctuation in stage occasioned by winter freshets. 

(4) Rough ice cover and piling up of ice due to quick water and rough bed. 



W'INTKK CONDITIONS. 



(5) Tendency for ice jams to occur, with eonsequenl backwater, etc. 

(6) St reams that remain open altogether or freeze over thinly for. short times, owing to — 

(ii) Exl remes of conditions as noted under (3). 

(6) High temperature, mainly in the southern portion of the area, suhjee! to 

ice conditions in winter. 

The above classification is intended for the ordinary winter. The 
winter of 1904-5 was much colder than the average, and many 
streams remained frozen over in places where ordinarily there would 
not be permanent ice. On the other hand, the winter of 1905-6 
was remarkably mild, and ice was carried away by freshets at many 
points where this very rarely happens. A gaging station, then, can 
be only approximately fixed in any of the above classes. 

The following tables summarize the winter conditions at 179 cur- 
rent-meter stations and 25 dam stations: 

Summary of winter conditions at current meter stations. 



Class. 



New Eng- 
land. 



New York 
and lower 
Michigan. 



Atlantic 
States. 



Central 
States. 



(1) Smooth, permanent ice cover 

(2) Tendency for anchor and needle ice to accumulate 

(3) Unstable ice cover 

(4) Rough ice cover and piling up 

(5) Tendency for ice jams 

(6) Remain open 



(a) 



(a) 
(a) 



33 



a Not reported in detail. 

Of the 179 stations considered 29 remain unfrozen thruout the 
winter, and at these stream flow can be estimated in the same manner 
as during the open season. Smooth, permanent ice cover is found at 
70 stations. The remaining 80 stations have miscellaneous conditions, 
all of which are probably unfavorable for estimating winter flow. 

Summary of winter conditions at stations at dams. 

Good conditions for estimates, crest unobstructed, ice cut away, or water mostly used 

by wheels 13 

Poor conditions for estimates, crest seriously obstructed 12 



25 



DURATION OF ICE SEASON. 



The following table gives the usual duration of ice cover in different 
areas where the streams freeze during the winter. 

Duration of ice cover, by areas. 



Locality. 


Date of closing in. 


Date of breaking up. 


Time 
frozen. 


Northern Maine 






Months. 
3J-5 


Northern Michigan 


December 1-30 




2 -3§ 

1J-3 

3"-4 


Lower New England 




New York 


December 1-15.. March 15-31 


Pennsylvania 






14-2J 

1 -2i 


Illinois 


December 15-January 15. . 


February 15-March 1. 
March 15-31 


North Dakota 


3J-4J 









10 



STREAM FLOW DURING THE FROZEN SEASON. 



A large amount of information relating to the duration of the ice 
season, especial^ with regard to lakes and navigable streams, was 
published in the report of the United States Deep Waterways Com- 
mission. a A few of the results for rivers there given are compiled in 
the following table : 

Duration of ice cover on northern sfreams. 



River. 



Locality. 



Connecticut , 

Do 

Hudson 

Illinois 

Merrimac 

Mississippi :. .; Davenport, Iowa 

Do St. Louis, Mo 

Missouri Bismarck, N. Dak 

Do Fort Buford, N. Dak. 

Ohio Cincinnati. Ohio 



Hartford, Conn 

Turners Falls, Mass. 

Albany. N. Y 

Peoria, 111 

Amoskeag, N. H 



Length 
of record. 



Years. 
42 
12 
87 
53 
- 18 
25 
31 
24 
15 
39 



Average date of- 



Closing. Opening. 



Dec. 12 
Deo. 9 
Dec. 15 
Dec. 17 
Nov. 28 
Dec. 12 
Dec. 19 
Nov. 25 
Nov. 15 
Jan. 15 



Mar. 12 
Mar. 16 
Mar. 20 
Feb. 21 
Mar. 19 
Mar. 19 
Jan. 20 
Mar. 31 
Apr. 13 
Jan. 25 



Time 
closed. 



Days. 
90 
97 
95 
66 
111 
97 
32 
126 
151 
10 



CHANGE IN THICKNESS OF ICE. 

After a stream becomes frozen over, the thickness of the ice usually 
increases rapidly, reaching a maximum generally by midwinter and 
then remaining nearly constant until shortly before the open-water 
season begins. As a rule there is some melting and thinning of the ice 
before it goes out, but a heavy early spring freshet may carry out ice 
at its maximum thickness. 

The following table shows the ice thickness at intervals through the 
winter at two fairly typical gaging stations. 

Thickness of ice on Connecticut River at Orford, N. H., and Esopus Creek at Kingston, N. Y. 



Date. 


Connecticut River at 
Orford, N. H. 


Esopus Creek at 
ton, N. Y 


Kings- 




1903-4. 


1904-5. 


1905-6. | 


1903-4. 


1904-5. 


1905-6. 




Feet. 


Feet. 

.3 
.7 
1.3 
1.5 
1.7 
2.1 
2.2 
2.1 



Feet. 


.1 



.7 


1.05 
1.15 
1.1 



Feet. 


Feet. 


Feet. 








. 5 
.95 
1.1 
1.25 
1.25 
.6 
«0 




: 6 4 5 

.6 

1.25 
1.5 
1.6 

.7 
«0 










.1 




.4 


January 15 

February 1 ^ 


1.7 

1.85 
1.9 
2.1 
+ 2. 



. 5 

.75 

.9 


Marcii 1 


.4 
.25 


March 30 


10 




- 



a March 31. 
SURFACE, ANCHOR, AND NEEDLE ICE. 

The three following forms of ice occur in streams and each of them 
affects the flow in a different way: (1) Cake, border, or surface ice; 
(2) needle ice, or "frazil," so called from the French word signifying 



a House Doc. 192, 54th Cong., 2d sess. 



WINTER CONDITIONS. 11 

"forge cinders," which are suggested by its dull, slushy appearance; 
(3) anchor ice, which closely resembles needle ice, Imi w hich is formed 
in ;i (lill'erent manner. 

Surface ice is formed when I he temperature of a quiet body of w ater 
becomes 32° F. As the maximum density of water occurs at 39.1°, 
the temperature of a quiel body of water thai is cooled from the sur- 
face will gradually increase from the surface downward after a genera] 
water temperature of 39.1° has been reached. Surface ice probably 
always begins to form at the shore or at the borders of solid objects 
and is extended by spicules shooting out and forming a network, the 
process being analogous to the growth of crystals in a saturated solu- 
tion except that ice is formed at the surface only. The surface layer 
of ice gradually increases in thickness and continues to grow as long 
as the air temperature is below 32° F. The rate of such increase 
varies with the temperature and other atmospheric conditions affect- 
ing heat radiation. The thickness of the ice layer increases in nearly 
direct proportion to the square root of the time. Surface ice also forms 
over smooth-flowing water, but as the velocity and roughness of the 
current are increased a condition is soon reached where the projecting 
ice needles are broken off as fast as they are foremd. 

It is obvious that the surface temperature of a stream passing over 
rapids where surface ice can not form would often fall below 32° F. 
if a portion of the water were not converted into ice in some manner 
and enough latent heat released to maintain the temperature con- 
stantly at 32°. It is well known that perfectly quiet water can be 
cooled below 32° F. without the formation of ice, apparently because 
the necessary nuclei and other conditions to start ice formation are 
not present. If, however, the slightest motion occurs, the water 
molecules are enabled to assume the arrangement necessary to crys- 
tallization and the water becomes filled with ice spicules. 

Elaborate experiments by Prof. Howard T. Barnes by means of an 
electrical-resistance thermometer indicate that flowing water in a 
stream can not be cooled more than one one-hundredth of a de«ree 
below the freezing temperature without the formation of ice. The 
ice spicules that form in agitated water vary in character with the 
variations in the rate of their formation. Elongated needles, cubical 
crystals, and broad, thin plates have been observed under different 
conditions. Apparently the stream may be filled with needle ice 
formed in the manner described without the flow being affected in any 
considerable degree. If, however, the needle ice is carried underneath 
the layer of surface ice, it forms an effective obstruction. 

Observations in St. Lawrence River indicate that masses of needle 
ice may travel under the surface ice for several miles. There is 
undoubtedly some frW through these masses, but the velocity is very 



12 



STREAM FLOW DURING THE FROZEN SEASON. 



slight. It has not been found possible to measure the flow through such 
ice with the current meter. The existence of flow is, however, indi- 
cated by the presence of impurities in the ice. A striking illustration 
of this flow is also given in fig. f , which shows two cross sections of 
Chemung River. At the upper section the channel underneath the 
surface ice was almost completely blocked by needle ice, while at the 
lower section, 200 feet downstream, there was but little needle ice; 



DISTANCE FROM INITIAL POINT 




DISTANCE FROM INITIAL POINT 

Fig. 1.— Cross sections of Chemung River at Chemung, N. Y., showing effect of needle ice. 

yet the observed velocities at the lower section were so great as to 
indicate that considerable flow through the masses of needle ice must 
have taken place. 

Gage readings or attempts to estimate the winter flow of streams 
at cross sections affected by needle ice are apparently worthless. 
Although the general features of ice formation in a given locality will be 
the same from year to year, a consideration of the conditions of needle- 



W1NTEB CONDITIONS. 13 

ice formation shows thai the differences will be sufficient to produce 
in affect a constantly changing regimen. The formation of needle ice, 
like that of surface or anchor ice, is due chiefly to radiation of heal 
from the water mass. Needle ice never forms underneath surface ice 
and is most frequently formed on cold, clear nights, when the heal 
lost by radiation is most greatly in excess of that received at the 
earth's surface. Professor Barnes states that the margin between the 
disintegration and the formation of the ice is exceedingly narrow, 
amounting to only a lew thousandths of a degree change of tempera- 
ture, the radiation and the absorption of the sun's rays by water being 
controlling factors. 

Snow falling on the surface of a stream becomes water-logged and 
forms a slush resembling floating needle ice. Snow crystals probably 
often form the nucleus of masses of needle ice, but the presence of 
snow is not an essential or important condition for the occurrence of 
such ice, as is sometimes supposed. 

Anchor ice is sometimes formed when stones or other objects in a 
stream are cooled by radiation to 32° F. It is a crystalline growth 
similar to needle ice and having the same density. It remains 
attached to the objects upon which it is formed as long as their sur- 
face temperature is below r 32°. Like needle ice, it forms most readily 
when the difference between radiation and absorption is a maximum. 
Apparently it never forms underneath surface ice; but whenever the 
relative loss by radiation is decreased, as, for instance, on a cloudy 
day, it may become detached and rise to the surface, carrying with it 
stones or other objects. It affects the regimen of streams chiefly by 
forming obstructions in portions of the channels that do not freeze 
over, thereby causing back water, or by rising and floating under- 
neath the surface ice, as needle ice often does. Anchor ice does not 
ordinarily form in streams with earth beds and apparently forms more 
extensively on dark-colored rocks, radiation from dark objects being 
greater than from light ones. 

RANGE OF WINTER GAGE HEIGHTS. 

Data regarding extremes of winter gage heights are given in con- 
nection with station descriptions (pp. 26-38). In general, winter 
freshets are uncommon in the northern portion of the area, in which 
the streams freeze and the range in stage is small, but the liability of 
their occurrence increases rapidly to the south. They are, however, 
usually not of long duration, and are not serious factors in winter 

oRept. Commission of Engineers on Floods, Montreal, 1890. Henshaw, Geo. H. Frazil ice: Trans. 
Canadian Soc. Civil Eng. vol. 1, pp. 1-23. Barnes, Howard T , Formation and agglomeration of frazil 
and anchor ice: Canadian Engineer, May, 1897, pp. 6-10; Formation of anchor ice and precise tempera- 
ture measurements: Trans. -Am. Soc. Mech. Eng., 1905. Ilorton, R. E., Anchor ice and frazi : Paper 
Trade Journal December 24, 1903. 



14 STREAM FLOW DURING THE FROZEN SEASON. 

estimates unless they are of sufficient size to cause the ice to break up 
and go out more or less completely, when the conditions of flow may 
become entirely changed. As a rule the regimen of flow changes less 
in winter than during the open season. 

FLOW OF STREAMS UNDER ICE COVER. 
GENERAL CONSIDERATIONS. 

In the Chezy formulas « 

Q = AV_ 

v=cvrs 

C is the coefficient dependent on the physical character of the 

stream bed and the hydraulic radius. The plrysical character enters 

into the determination of C in the form of a coefficient of roughness, 

n. The relation of n, R, and C, as deduced by Kutter, is as follows 

(for English units) : 

A , nn 1.811 0.00281 

41.66+—— + 5 — 

p_ n o 



( 4 , 66+ -§-)3 



yVR 

It will be seen that for a given slope and hydraulic radius the mean 
velocity of a stream is nearly proportional to 1 s-n; that is, the velocity 
is inversely proportional to the roughness of the stream bed. The 
Chezy and Kutter formulas are empirical and in their application 
values of n determined from previous experiments are selected by 
judgment. 

FRICTION DUE TO AIR AND ICE. 

If V, R, and S are given, the value of n may be calculated from the 
Kutter formula. In such calculations for open-channel conditions 
the hydraulic radius is taken as the ratio of are.a of cross section to the 
wetted perimeter, not including the surface in contact with the air. 
It is probably true, however, that the mean velocity of a stream is 
usually less than it would be if there was no friction between water 
and air. 

If the air-contact surface is replaced by a film of ice, then, in making 
a calculation of C or of the velocity, the entire wetted perimeter, 
including that portion of the boundary of the stream section in con- 
tact with ice, would naturally be included in calculating the hydraulic 
radius. 

If the value of n is derived by considering the wetted perimeter as 
including the air and ice contacts as well as those of bed and banks, 
and if the frictional resistance of the water-ice contact is greater than 



STREAM FLOW UNDER 10E. 15 

(ho friotional resistance of the water-air contact, then n will have a 
correspondingly greater value for conditions of ice cover than for 

those of open channel. In other words, the ice cover increases total 
friction by an amount representing the difference between air and ice 
resistance and not by an amount representing the total ice friction. 

The ordinary friction of a stream bed may he considered as made 
up of two parts — (1) skin friction and (2) internal motion. 

In most instances a film of water adheres to the surface of solid 
objects over which the water Hows, and the skin friction between the 
water and these objects is essentially the same as that between two 
fluid surfaces. It is measured by the viscosity of the liquid, the 
energy absorbed probably being for the most part converted into 
heat. 

If the stream bed is rough, the impact of the water creates swirls or 
eddies, in which a portion of the energy is converted into internal or 
vortex motion not useful in causing forward motion. 

So far as known, no experiments have been made relative to the 
skin friction of a smooth ice surface. It may be assumed, however, 
to be about the same as for a smooth glass or planed- wood surface, 
especially the latter. A layer of water adheres to such a surface or is 
entrapped by the capillaries, so that the friction surface is essentially 
a layer of liquid particles, the conditions thus closely resembling 
those where water at 32° F. is in contact with ice. 

The value for glass or planed-w T ood surfaces of n in Kutter's formula 
is given by various authorities as about 0.009, or from one-fourth to 
one-third the resistance due to an ordinary stream bed. When the 
under ice surface is rough, broken, tilted, or honeycombed, its impact 
resistance may become of the same or even greater relative impor- 
tance than that of an earth or rock surface. It is presumable that 
cases are rare where the under surface of the ice cover is so free from 
irregularities as to give a value of n as low as those applying to glass 
or planed wood. 

Occasionally a layer of needle ice of varying thickness floats under 
or accumulates on the lower surface of the ice cover. Such ice not 
only obstructs the flow through the portion of the cross section 
occupied, but also greatly increases the friction as compared with 
that of a smooth ice surface. 

RELATIVE IMPORTANCE OF AIR AND ICE FRICTION. 

As already pointed out, the actual increase in friction due to an ice 
cover is the difference between the ice friction and the air friction pre- 
vious to the formation of the ice cover. Owing to the divergent 
opinions entertained as to the magnitude of air friction, it has been 
thought well to discuss the matter somewhat at length. 



16 STREAM FLOW DURING THE FROZEN" SEASON. 

In the Chezy formula and in most other similar slope formulas it 
is assumed that all the resistance to the motion of the water proceeds 
from the stream bed. Humphreys and Abbot a found, however, 
that the position of the point of maximum velocity in vertical velocity 
curves on Mississippi River was controlled by the direction and veloc- 
ity of the wind. They give the following expression: 

^=(0.317+0.06/) D 

In this formula D = depth in feet; d=depih of point of maximum 
velocity; /= relative wind velocity on a scale such that a calm = 
and a hurricane=10. 

In deriving a formula for the mean velocity of streams in terms of 
the slope and hydraulic radius, Humphreys and Abbot assumed that 
the frictional resistance between the water and air contact surfaces 
was similar in nature and magnitude to the bed resistance. In their 
formula, accordingly, the hydraulic radius is expressed as follows : 

R- A 

F+W 

In this formula A = area of cross section, P = wetted perimeter in 
earth, W= width of surface. 

In discussing the results of Humphreys and Abbot's investigations, 
the late James B. Francis made the following clear statement as to the 
effect of air friction : b 

When the air in contact with the surface of the water flowing in an open channel is moving 
in the same direction and with the same velocity as the surface of the water, it is clear that 
it can have no effect on the motion of the water; but such exact conformity in the motion of 
the air and water is uncommon; ordinarily the air has some motion relatively to that of the 
water and either retards or accelerates the velocity of the surface. That the air may pro- 
duce a material effect on the scale of velocities is apparent from the following considera- 
tions. 

Let us suppose the surface of the water to move, relatively to the air, with the same 
velocity that the water at the bottom moves relatively to the bed ; also that the inequalities 
of the surface of the water caused by the action of the air and those in the bed of the stream 
are alike; and suppose, also, that a sheet of water of uniform thickness, in contact with the 
bed, is at rest; we shall then have the water near the bottom moving over a bed of water 
and the water at the surface moving under a bed of air, and as both beds have the same 
inequalities, they will cause the same retardation in the velocity of the water, except as 
these beds, from the nature of the substances of which they are composed, offer more or 
less resistance. These resistances will be of the same nature as is experienced by a body 
moving in a resisting medium. According to well-known principles, the retardation in 
this case is as the square of the velocity of the moving body relatively to that of the medium 
and as the density of the medium. The density of the air is about ^^ of that of water; a 
body moving through the air with the same velocity will therefore be retarded -g^ as 
much as if it moved through water. 

The above conclusions are confirmed by a comparison of the coef- 
ficients that have been determined experimentally for use in comput- 

a Physics and Hydraulics of Mississippi River, p. 305. 
t> Lowell Hydraulic Experiments, pp. 158-159. 



STREAM FLOW UNDEB K - K. 



17 



inglossof pressure occasioned by the flowing of air and water through 
pipes, the term of expression adopted by Weisbach being used: 

P=f d~2g 

In I his fornlula /' loss of pressure in pounds per square inch; / = 
length of pipe in feel ; </ diameter of pipe in inches; r -mean veloc- 
ity in feet per second; f coefficient of resistance to How. 

Rough average values of t he coefficient /', according to Weisbach's 
experiments, may he taken as follows: For air, f= 0.000 160; for 
water, /= 0.1 04, the relative friction loss for water being 650 times 
that for air. 

It seems probable, then, that with still air the frictional effect of air 
on water surface is hut a small percentage of that due to stream bed, 
although with a strong wind upstream the retardation of the filaments 
of water near the surface may he considerable. 

VARIATION IN SLOPE DUE TO FREEZING. 



As an ordinary stream is made up of smooth-water reaches sepa- 
rated by more or less pronounced rapids, and as the swiftest por- 
tions of a stream freeze least readily, the freezing of a stream will 



„+/, ice cover Jt- --^"^ 
S t- ^tfiffffl 


^fff0'' 






jfffjl' 





Fig. 2.— Effect of freezing on a smooth section of a river terminated by rapids. 

lead to the following conditions: (1) There will be an increase in the 
total friction due to replacing the water-air contact surface by water- 
ice contact surface; (2) if the discharge remains the same, it follows 
that with increased friction either the slope or the cross-sectional area 
must increase. 

In a long, uniform channel, frozen throughout, there can be but little 
or no increase in slope ; but in short reaches separated by open water, 
such as those where gaging stations are commonly located, an appre- 
ciable local increase in slope due to freezing may easily occur, as 
shown in fig. 2. As a result of freezing of the smooth-water reach 

irr 187—07 2 



18 STREAM FLOW DURING THE FROZEN SEASON. 

M N there is a tendency for the stage to be raised, as shown by the 
dotted line, and the upper stretch of quick water above N may be 
partly submerged by backwater. If the discharge remains the same 
the depth of open water at M will not be increased unless there is 
backwater here due to ice cover below this point. If the depth at M 
is not increased, the fall of the water surface between N and M will 
have been increased. There is no actual increase in slope, except in 
the vicinity of M, and the ice surface adjusts itself parallel to the 
channel bed, as in the case of flow in an open channel, but the effective 
fall from N to M is of course increased. 

CHANGE IN AREA OF WATERWAY REQUIRED BY FREEZING. 

The conditions that occur when a broad river becomes covered 
with a uniform ice surface are illustrated by the following example: 
Consider a rectangular channel in which the width B D is many times 
the depth, so that the wetted perimeter may be taken as approxi- 
mately equal to the width. Neglecting the air friction, call the coef- 
ficient of roughness applying to the channel n v Consider also that 
the cover E F may be brought just in contact with the stream surface, 
the coefficient of roughness for this ice cover being n 2 . The slope and 
discharge being assumed to remain constant, the effect of cover of 
varying roughness may be illustrated as follows : 
Let width B D =500 feet, 

slopeS =0.0005, 

depth D =5 feet, 

area of section = 2,500 square feet, 
wetted perimeter = 500 feet approximately, 
hydraulic radius = 5 feet approximately. 
Then for n = 0.030, as in an ordinary river, the mean velocity 
would be 3.29 feet per second, and the discharge would be 8,225 
second-feet. 

If, now, the stream is covered over, if n x and n 2 equal 0.030 each, 
and if the discharge is the same as before, then the stream stage must 
evidently rise in such manner that the increase in C, resulting from 
increased hydraulic radius, together with the increase in R and A, will 
counterbalance the increased friction. Owing to the complexity of 
the Kutter formula, the result can best be determined by successive 
approximations rather than by analysis. 
We will have, if D remains as before, 

R = 2.5 V=2.01 Q=5,025 

If D is increased 1 foot, 

11 = 3.0 V = 2.29 A= 3,000 Q= 6,870 

If D is increased 2 feet, 

R = 3.5 V = 2.56 A = 3,500 Q = 8,960 

By interpolation between the last two values it appears that the 



STREAM FLOW UNDER K'K. 1 \) 

stage inusl increase about L. 65 feel in order thai the discharge shall bo 
the sai nc as for open channel, [f, on the other hand, the value of n 2 for 
the covered surface was 0.010, then since the wetted perimeter for 

tin' hod ami for iht 1 covered surface are approximately the same, the 

average coefficient of roughness for the entire stream section would be 

o.oio h0.030 

- = 0.02 

With t his value of a, in order to give t lie origina] discharge of 8,225, 
the stage would need to be raised about 0.2 foot. 

In actual streams the wetted perimeter of the stream bed will 
usually be somewhat more than half of the total cross-sectional bound- 
ary: furthermore, as shown elsewhere (pp. 14-15), when the stream is 
covered, the effect is to replace air-surface friction by ice-surface fric- 
tion: so that, all things considered, the presence of a thin, smooth ice 
cover will probably not necessitate any very great increase in stage in 
order to maintain the discharge undiminished. 

As a river becomes nearly or, quite frozen over and the thickness of 
ice increases, the diminution of area of water may be considerable. In 
the example previously quoted, for the given stage the area of 
waterway would be reduced as follows (if the ice is floating) : 

Effect of thickness ofia mi una of waterway. 



Thickness 
of ico. 


Reduction in area of 
waterway. 


Feet. 
0..5 
1 
1.5 

2 


Sq. //. Per rt a!. 
230 9.2 
460 is. 4 
690 27.6 

•920 36. S 



With ice 2 feet thick, then — which is not uncommon — there would 
be a reduction in area of about 37 per cent. In the example, above, a 
rise of stage of 0.2 foot was occasioned by T thin ice cover. With 2 feet 
thickness of ice a further rise of about 1.84 feet, with no snow load 
upon the ice, would be required to insure the same discharge. The 
total necessary rise of stage would then be 2.04 feet. 

EFFECT OF THICKNESS OF ICE ON FLOW. 

It is evident that the discharge for a given gage height, taken to the 
water surface where there is a thick ice cover, may be diminished very 
materially as compared with that for open-water conditions. 

By further considering the data on page 18, and also assuming a 
change in depth (or gage height) from 5 to 8 feet, we obtain the 
following : 



20 



STREAM FLOW DURING THE FROZEN SEASON. 



Relation of gage height to discharge. 
[S = 0.0005; n = 0.030 for open water; n = 0.020 for thin ice cover.] 



Depth 

(or gage 
height). 


Discharge 
(open sec- 
tion). 


. Discharge under ice cover. 
lo Discharge for open section. 


ThtaI »- Ic thick ot 


Ice 2 feet 
thick. 


Feet. 

5.0 
6.0 
7.0 
8.0 


Second-feet. 
8,225 
11,200 
14, 500 
18, 200 


0.91 
.91 
.92 
.92 


0.65 
.70 
.73 

.74 


0.42- 
.49 
.55 
.59 



For the rectangular section as chosen this indicates that for a given 
stage the ratio of discharge under ice cover to that for open section 
diminishes as the ice thickness increases; for thin ice cover it is 















\ 

















































0.50 

RATIO 



0.60 0.70 0.80 

DISCHARGE UNDER ICE COVER 



DISCHARGE FOR OPEN SECTION 
Fig. 3. — Effect of change in stage on discharge under ice cover, with varying thickness of ice. 

approximately constant for ordinary stages, but as the ice thickens, 
the effect on the ratio is much greater at the lower gage heights. To 
further illustrate this tendency, fig. 3 has been prepared. The proper- 
ties of the gaging cross section of the Connecticut River at Orford, 
N. H., are here used (at gage height 4.0; area = 1,280; width = 267; 
hydraulic radius = 4.76; slope assumed as 0.00012; n =0.035 for open- 
water conditions; and w =0.025 for channel frozen). Under these 
assumptions with thin ice, the relation between discharge under ice 



OBTAINING WINTKK RECORDS. L' 1 

cover ..ml thai for open water is nearly constanl for ordinary stages; 
for thick ice this relation may vary 25 or 30 per cenl in this range of 
gage heights (which is about the usual winter range at (his station), 
the tendency being for this ratio to increase as gage heights increase. 

The effect of a thickening ice cover for given conditions of slope and 
roughness and for a given gage height is as follows: (1) To diminish 
the cross-sectional area; (2) to slightly diminish the wet led perimeter, 
by lessening the width; (3) to decrease the hydraulic radius as a resull 
o\' the loss of area while the wetted perimeter changes only slightly. 

Changes of area and hydraulic radius both tend to diminish flow. 
It is evident that the relative effect of this diminution will become less 
and less as stage increases, for both area and hydraulic radius increase 
directly as the gage height, while th°i loss of area and hydraulic radius 
for a given thickness of ice is approximately the same at any ordinary 
stage. 

METHODS OF OBTAINING WINTER RECORDS. 

CURRENT-METER STATIONS. 
GAGE HEIGHTS. 

Previous to the winter of 1903-4 records of gage heights for the 
frozen season were not in general obtained, the exception being in the 
case -of a few gaging stations on Catskill Mountain streams in the 
vicinity of New York City, where the attempt was made to procure 
continuous records from the time of their establishment in 1901. 
Since 1903 gage heights have been procured during the winter at a 
considerable number of stations in the Eastern and Central States. 
An effort has been made to obtain data bearing on both the stage of 
the river and ice conditions. 

The observer is not expected to read the gage and obtain the attend- 
ant ice data oftener than once or twice a week unless unusual condi- 
tions prevail (such as high water, due to rains or melting snow), as the 
change in stage under ice cover is usually a slow and even one. The 
essentials in these observations are as follows: (1) A hole is cut in the 
ice at (or underneath) the gage, the gage is read to the water surface 
and to the top of the ice, and the thickness of the ice is measured; (2) 
any special conditions are noted, either in remarks or by sketch, such 
as areas of open water, backwater effect due to ice jams, etc. Observ- 
ers are instructed to measure the thickness of ice occasionally at other 
places in the cross section at the gage and at points up and down 
stream. For these winter duties observers are furnished with an ice 
chisel and an ice-measurement stick, so arranged with an L end that 
the bottom of the ice can be definitely located and the thickness noted. 

The transition periods from open channel to frozen conditions in the 
fall and the reverse in the spring are important. During the fall- 
transition period, while the river is freezing, two methods have been 



22 STREAM FLOW DURING THE FROZEN SEASON. 

used for gage readings, as follows : ( 1) Daily gage readings to the top 
of the ice are made continuously, until the ice is strong enough to 
walk on, the date of first freezing having been noted. After the ice 
cover forms the usual winter observations begin, as previously 
described. (2) The ice is broken daily under the gage, a good-sized 
hole being made with a weight and rope provided for the purpose, and 
gage heights are read to the water surface, until the ice is strong 
enough to walk on, when the thickness can be noted and the usual 
method followed. 

In spring when the ice goes out daily gage readings begin with any 
considerable increase in stage and conditions as to ice — time of ice 
going out and of river being clear from ice, etc. — are noted. If at any 
time during the winter high water occurs or the ice goes out, daily gage 
readings are resumed until steady conditions" once more prevail. 

CURRENT-METER DISCHARGE MEASUREMENTS. 

Holes are cut in the ice at points in the cross section where it is 
desired to obtain velocity determinations. These holes can be cut 
usually to best advantage with an ice chisel and are made only large 
enough to allow the ready lowering of the current meter through them. 
A rectangular hole 12 by 24 inches, with its length in the direction of 
the cross section and with vertical sides, has been found convenient 
for thick ice; lesser dimensions may be used where the ice is thin. In 
a few cases it has been necessary to cut a continuous channel between 
two or more adjacent holes, especially where the holes are close 
together, to prevent rapid vertical pulsations of water in the holes. 
Where a large number of holes are to be cut, a special auger cutting 
out a cylindrical core of ice has been used to advantage by United 
States Army engineers. The auger is driven by hand, by means of 
a suitable framework and gearing, similar to a carpenter's frame bor- 
ing machine. 

The cross section at which open-water discharge measurements are 
made is always used, when possible, as more direct comparisons can 
thus be made of the various features of flow under ice cover, with 
similar data for open channel. If, as sometimes happens, it is desir- 
able that the measurements of flow under ice cover be made at a 
different or auxiliary section in order to obtain more favorable condi- 
tions, it is necessary to install an auxiliary gage or reference point, or, 
by sufficient soundings at the section used to keep control of the area, 
positions of ice surfaces, etc. 

Soundings are always referred to the surface of the water in the 
holes, and, in addition, the distance from the water surface to the top 
and the bottom of the ice is noted. The depth of snow covering the 
ice, if any, is also noted and if possible a determination made of its 



OBTAINING WINTER RECORDS. 23 

water equivalent. The character of the ice and of its under surf <•<• 
is Doted, especially with regard to smoothness. 
Gage heights are taken to the water surface and the top of the ice 

in the same way as by the observer, but, in addition, especially if an 
auxiliary section is being used for the current meter, holes are cu ! in 
the gage cross section and a little distance up and down stream in 
sufficient number to get a good average determination of the thick- 
ness of the ice and its position relative to the water surface. 

Velocity observations have been most generally made by the ver- 
tical velocity-curve method, or at least a sufficient number of curves 
have been obtained to give good control of any single or double 
point method. Vertical velocity curves have also been very fre- 
quently taken for the reason that data were thus obtained for study 
and for the devising of shorter methods of observation. 

A double-point method giving good results was developed from 
data obtained in 1904 and was used in measurements for the next 
two seasons. This consists in making observations at 0.2 and 0.8 
of the total depth (below the bottom of the ice), the mean of these 
two velocities being very nearly the mean velocity" of the vertical. 

Single-point methods, in which the velocity is determined at 0.4, 
0.6, or mid depth, are sometimes used, it being necessary to have 
vertical velocity curves at the same points and taken under similar 
conditions in order to deduce the mean velocity from the observed 
velocity. 

Vertical integration has been used to a limited extent, but it has 
not been found as convenient as the methods previously described 
and it gives no data for the study of the vertical velocity curve. 
It is also objectionable owing to the difficulty of properly handling 
the current-meter cable, which becomes wet and covered with ice. 

The horizontal distance between velocity observations should 
probably be about the same as for open w r ater for the best results, 
but frequently it is advisable to extend it somewhat beyond that 
limit, in order to reduce the labor required for cutting holes in the ice. 

The current meter is used either suspended by a cable in the 
ordinary manner or fastened to a w T ooden or metal rod. If a cable 
is used, it is marked at intervals of 0.5 or 1 foot by small lengths of 
cord wound and tied about it for use in sounding and placing the 
meter. It is most convenient to refer these to the center of the 
meter and add to soundings the distance from the center of the 
meter to the bottom of the weight. If a rod is used (this is of 
course limited to comparatively small depths and low velocities), 
it may be graduated from the center of the meter in a similar way. 
The rating of the small Price meter when it is fastened to a rod, 
but free to tip on its horizontal axis, is almost identical with that 
when the meter is suspended by T a cable in the usual way. 



24 



STREAM FLOW DURING THE FROZEN SEASON. 



The meter must be kept in the water continuously, or nearly so, 
if the temperature of the air is much below freezing, as ice will 
form very quickly on exposure and perhaps cause the meter wheel 
to stick. If the temperature is very low, trouble is also experienced 
from ice gathering on the cable or rod supporting the meter. 

Measurements during inclement weather can often be most con- 
veniently made under a shelter consisting of a framework of light 
boards or poles covered with canvas. A cross plank at a height of 
about 3 feet serves as a convenient support for instruments and 
stop watches, as well as a datum for lowering the meter in making 
vertical velocity curves. 

In moving from station to station the meter is drawn up until 
it clears the ice and left suspended from the cross plank while the 
entire shelter is carried forward to the next point of measurement. 
By this method the necessity of handling the wet cable, often trou- 
blesome, even when rubber mittens are used, is generally avoided. 

The additional cost of measurements on frozen streams over that 
for the open season is occasioned by the following conditions: (1) 
General difficulty of field work during cold weather, and conse- 
quently longer time required; (2) labor required to cut holes in ice 
and perhaps clear off snow; (3) longer methods required in gaging. 
The following table gives data regarding the cost of gaging under 
ice cover at certain stations during 1904-1906 as compared with the 
cost of gagings made under open-water conditions. 

Cost of current-measurements under ice cover. 











Average 














cost per 




Usual 


Locality. 


Number 

of 
stations. 


Year. 


Number 

of 
gagings. 


gaging, 
exclusive 
of travel. 
to and 
from 
station. 


Average 

total 
cost per 
gaging. 


total 

cost per 

gaging, 

river 

open. 




1 

* 3 

4 

9 


1904 
1905 
1906 
1906 


4 
7 
19 
15 


$30. 52 
16. 67 
14.18 
18. 24 


$34. 64 
18.82 
15. 65 
22.13 


$10. 00 


Do 


8.57 


Do 


10. 42 




10.32 







The ".usual total cost per gaging, river open," is based on a record 
of actual costs during 1904 and 1905 for New England and from 
July, 1904, to Juty, 1905, for New York stations. During the 
greater part of the 1906 winter gagings in New England only one 
hydrographer was in the field, laborers being employed for the 
work of cutting holes in the ice and assisting in gaging. Previous 
to that time there were usually two hydrographers. All New York 
gagings have been made by two hydrographers. 

The average cost per gaging for ice cover, exclusive of travel, is 
from one and one-half to three times that for open-water conditions. 



U. S. GEOLOGICAL SURVF 



.■.aim: ■ iicplY PAPER NO. 187 PL. 




A. GAGING STATION ON SANDY RIVER AT MADISON, ME., AT DAM OF MADISON 
ELECTRIC COMPANY 




B. GAGING STATION ON WINOOSKI RIVER AT RICHMOND, VT. 



OBTAINING WINTER RECORDS. 25 



STATIONS AT DAMS. 



A considerable number of the gaging stations of the Survey are at 
water-power plants, and records are obtained by observing the How 
over the dam. i he wheel-gate openings, etc., and the amount of water 
used by wheels. 

During cold weather ice may form in large quantities on the crest of 
a dam and vitiate the computations made from gage heights of flow- 
over the dam. PL I, A, gives an excellent illustration of the manner 
in which ice may form upon a dam. This plate shows one of the regu- 
lar stations of the Survey at Madison, Me. In some cases this diffi- 
culty can be obviated by keeping the ice cut away from the crest, as 
is frequently done at an electric-light and power plant; or where that 
is impracticable, a record of ice conditions, with proper corrections, 
may serve to make approximate estimates. 

The flow through turbines is as easily determined in winter as in 
summer. Frequently the greater part of the flow is taken through the 
wheels. Gaging stations at dams and mills usually afford better 
opportunities for securing winter records than exist at many current- 
meter stations. 

ESTIMATES FROM PRECIPITATION. 

Methods of estimating stream flow from precipitation are so gener- 
ally known as to require no detailed explanation. In most such esti- 
mates the run-off in any month is determined from the contempora- 
neous precipitation by the use of a ratio or reduction factor. In crude 
estimates it is assumed that a constant percentage of the precipita- 
tion will appear as run-off regardless of the amount of precipitation. 
In more exact work a sliding scale of coefficients is used, the values 
depending on the amount of precipitation and the month or season. 

For precipitous and impervious basins the run-off will be nearly 
coincident with the precipitation. If, however, there are lakes, for- 
ests, extensive ground-water storage, or accumulated snow within the 
basin, the precipitation in one month may not appear as run-off for a 
considerable interval of time, and any attempt to estimate the run-off 
for any month from the contemporaneous precipitation will be value- 
less. This is especially true in basins where much of the winter pre- 
cipitation is in the form of snow, which accumulates on the ground, 
especially in ravines and forests, so that water representing several 
inches depth on the drainage basin may be carried forward from 
month to month, or from one calendar year to another, without enter- 
ing the stream. 

A heavy precipitation in the form of snow may occur without any 
appreciable effect on the stream flow. Oil the other hand, whenever 
the temperature rises above 32° F., run-off from melting snow occurs, 



26 STREAM FLOW DURING THE FROZEN SEASON. 

and often the entire winter's snow storage enters the stream in the 
course of a few days. During from one to three months of the 
spring freshet season northern streams generally show a run-off con- 
siderably in excess of the contemporaneous precipitation. 

Data regarding the evaporation loss from snow-covered surfaces 
are very meager. If records of the snowfall, snow accumulation, and 
temperature are at hand it may be possible to form estimates of the 
total run-off of a stream for the winter season. It is obviously impos- 
sible at present to form reliable estimates of winter flow for shorter 
periods from precipitation data alone in any manner similar to that 
commonly used in estimating the flow from the rainfall during the 
summer months. 

The minimum flow of a stream, either in summer or winter, ordi- 
narily occurs at times when there is no direct surface run-off and when 
the permanent supply from ground water, lakes, or storage reservoirs 
is at a minimum. 

The presence of snow with low temperature effectively cuts off 
direct surface inflow in winter, sometimes for a period of several 
months. Careful studies of the laws of supply to a stream from 
ground water during either summer or winter droughts will be of value 
in estimating the winter regimen. 

With present knowledge it is evident that actual measurements of 
flow from gagings are even more needful in winter for the determina- 
tion of available water supply from streams than in summer, although 
in the existing data of stream flow the winter period is to a consider- 
able extent neglected. 

WINTER RECORDS. 

Data on open-water and winter conditions and the discharge 
measurements made during the frozen season are here given for the 
following stations :' 

Catskill Creek at South Cairo, N . Y. 
Connecticut River at Orford, N. H. 
Esopus Creek at Kingston, N. Y. 
Fish River at Wallagrass, Me. 
Kennebec River at North Anson, Me. 
Rondout Creek at Rosendale, N. Y. 
Wallkill River at Newpaltz, N.-Y. 
Winooski River at Richmond, Vt. 

CONDITIONS AT STATIONS. 
CATSKILL CREEK AT SOUTH CAIRO, N. Y. 

This station was established July 4, 1901. It is located at the 
highway bridge in the village of South Cairo, about 1 mile north of the 
Catskill Mountain Railroad station for that place. The drainage area 



wiviKK RECORDS. 2 i 

is 2G3 square miles. Measurements are made from the downstream 
side of ilic bridge at ordinary and high stages, and l>\ wading a shorl 
distance above the bridge a1 low stages. 

The drainage basin of this stream receives the run-off from the 
north slope of the Catskill Range and lies for the mosl pari in the tim- 
bered highlands of Greene County. The source of the creek is in a 
swamp at Franklinton, Schoharie County. It enters Hudson River 
at Catskill after traversing Greene County for nearly 25 miles. The 
stream Hows over a rocky bed through the greater part of its course, hav- 
ing a total fall of 1 ,200 feet. At the station the bed consists of gravel 
and rock, ihe main channel lying nearest the right-hand abutment of 
the bridge, which has a clear span of about 194 feet. About two- 
thirds of the way across is a gravel bar covered with brush which 
affects the discharge to some extent in high water and at low-water 
stages rapids about 1,800 feet below the bridge tend to cause slack 
water at the regular section for gaging. Both banks are high and ot 
subject to overflow'. The left bank is wooded; the right is rocky and 
abrupt. Below the bridge the stream is fairly straight for about 
1,000 feet; it then curves to the left and flows over some rifts, which 
at ordinary stages narrow the stream from about 200 to about 30 feet. 
Above the bridge the course is straight for about 500 feet; there is 
then a slight turn and some rapids that narrow the channel down to 80 
or 90 feet, the width at the bridge being about 125 feet. A portion of 
the stream bed is permanent, the gravel bar on the left-hand side hav- 
ing a tendency to shift. 

From Hudson River to the mouth of Kaaterskill Creek, about 2 
miles, there is practically no velocity. From Kaaterskill Creek to 
Leeds, 3 miles farther up, Catskill Creek flows through a gorge of blue- 
stone, in which it has a fall of about 180 feet. Two dams formerly 
utilized a portion of this head at Leeds. There is no interference at 
the station, however, as it is about 3 miles farther up. The extreme 
stages observed are as follows : 

Extreme, stages observed on Oatskill Greek <if South Cairo, V. )' . 

figrt. Discharge. 



Feet. 

High water 11.7 

Low water 2.25 



Second-fi < t. 
18,600 

is 



Extreme rango 



is,r>S2 



Catskill Creek in this vicinity usually freezes over about December 1, 
and the general breakup conies about March 1 , the stream being 
partly free from ice for short periods in January or February durirg 
what is commonly known as the January thaw. The entire width is 
usually frozen from a point 500 feet above the station to a point about 



28 STREAM FLOW DURING THE FROZEN SEASON. 

1,500 feet below; the rapids seldom freeze except in the coldest 
weather. Needle ice is produced in abundance in this stream, the 
observer reporting that the channel is obstructed by this kind of ice 
for the greater part of the winter. 

Ice conditions on CatsMU Creek at South Cairo, N . Y . 

SEASON OF 1903-4. 

November 29, ice 0.6 foot; practically the same up to December 13. 

December 17, ice at gage 0.88 foot. 

December 19, ice at gage 1 foot. 

December 20, rains; creek broken up. 

December 27, ice at gage 0.25 foot. 

December 31, ice at gage 0.6 foot. 

January 1-22, ice averaged about 0!65 foot. 

January 23-26, inclusive, ice broken up. 

January 27 to February 8, ice from 0.1 to 0.6 foot thick. - 

February 9, heavy thaw; ice went out. 

February 16 to March 3, ice from 0.2 to 1 foot thick. 

March 8, heavy rains; ice went out. 

SEASON OF 1904-5. 

November 27, ice 0.1 foot thick. 

December 1-7, ice 0.2 foot thick, increasing to 1 foot by December 27. 

December 28, creek broken up. 

January 5, creek filled with anchor ice. 

January 7, anchor ice broken up. 

January 15, creek filled with anchor ice. 

January 25-28, ice 0.5 foot thick; stream frozen across to about same thickness both 
above and below gage. Observer states that stream is filled with anchor ice attached to 
bottom, except in narrow strip along gage. Conditions continued the same for three weeks 
with exception that general ice thickness increased from 1.2 feet upstream to 1 .5 feet down- 
stream from gage. 

February 18, stream frozen over except along right bank, where ice becomes honey- 
combed and is broken. 

Februarjr 25, stream frozen across both above and below gage 1.08 to 1.25 feet thick. 
Observer states that ice is gradually melting, and shows channel near left bank below gage. 

March -1, ice throughout 0.83 to 1 foot thick, but narrow channel on each side. 

March 19, ice broken up. 

SEASON OF 1905-6. 

December, some ice about the middle of the month, but river not frozen solid. 

January 8, ice about 0.17 foot thick. 

January 9-11, ice 0.25 foot thick. 

January 12-14, ice 0.33 foot thick. 

January 15, ice 0.25 foot thick 

January 24, ice broken up. 

February 1, about 0.83 foot of ice both above and below gage, also at gage. 

February 22, ice broken up. 

February 28, creek filled with anchor ice, both above and below gage. 

March 5, ice went out about this date. 



WINTKK RECORDS. 



29 



The range of winter gage heights and maximum thickness of ice 
observed are as follows: 

Rang* oj wintei </<"/< heights and maximum fin cirrus* of [a <m Uatskill. ('ml: ai South 

Cairn. X. )'. 



Date. 



I!HU 2 

1902 3 

1903 1 
L904 5 
190S G 



Gage height to water surface. 


Minimum. 


Maximum. 


Range. 


Feet. 


Feet. 


Feet. 


2. 90 


4. 82 


L.92 


3.08 


4.90 


1.82 


3. 10 


4.55 


1 . 45 


2.80 


3.05 


. 25 


2. 70 


5. 15 


2. 45 



Ma \ ii 

thickness 
of ice. 



Feet. 



1.37 
.16 
.54 

.17 
. 83 



CONNECTICUT RIVER AT ORFORD, N. II. 

This station was established August 6, 1900. It is located at the 
wooden highway bridge between Orford, N. H., and Fairlee, Vt. 
The drainage area at this point is 3,305 square miles. Measurements 
are made from the downstream side of the highway bridge. 

The bed of the stream consists of gravel and is permanent. Both 
banks are high and do not overflow. At the bridge the channel is 
about 275 feet wide at ordinary stages and is broken by one pier. It 
is straight for 1,000 feet above the station and for a considerably 
longer distance below. The channel is about the same width both 
up and down stream, but at the bridge this width is cut down approxi- 
mately 13 feet by the pier. 

Several small streams enter the Connecticut near Orford, but the 
only stream of any considerable size is Waits River, about 5 or 6 miles 
above this point. The nearest dam is at Wilder, about 18 miles down- 
stream. Backwater effect from this dam reaches probably within a 
few miles of Orford. Upstream the nearest dam is at East Ryegate, 
about 20 miles above Orford. There is considerable fall in the river 
in this 20-mile stretch, although it is somewhat concentrated at a few 
points. The extreme stages observed are as follows: 

Extrt mi stages observed on Connecticut Hirer at Orford. N. II. 



High water 

Low water 

Extreme range 



Gage 
height. 



Discharge. 



Feet. Second-feet. 

26.1 03.000 

2. 640 



24.1 ! 



02,360 



30 



STREAM FLOW DURING THE FROZEN SEASON. 



Connecticut River in this vicinity usually freezes over about 
December 1 and remains frozen until the middle or last of March. 
Near the bridge ice first forms at the shores and around the pier, the 
left channel always freezing over first and the right channel some- 
what later. This portion of the river — from the dam at- Wilder to 
quick water at or above Wells River — has usually a permanent ice 
cover during the winter months. Anchor or needle ice has never 
been found here in sufficient quantities to affect gage heights or inter- 
fere with gagings. 

During the season of 1905-6 the river was completely frozen over 
at the Orford bridge only from about December 30 to January 24, 
when a rise in stage .carried out the ice. It did not freeze entirely 
across again during the winter. An area about 1,000 feet long and 
150 feet wide, nearly in the middle of the river and extending down- 
ward from the bridge, remained open. 

Ordinary winter conditions are good at this station, and the range 
of gage heights is small. Occasionally a winter freshet such as those 
of December, 1901, and January, 1906, occurs, but these usually last 
only a few days. The range of winter gage heights and maximum 
thickness of ice observed are as follows : 

Range of winter gage heights and maximum thickness of ice on Connecticut River at Orford, 

N.H. 



Date. 


Gage height to water surface. 


Maximum 

thickness 

of ice. 


Minimum. 1 Maximum. 


Range. 


1900-1 


Feet. 
5.8 
3.S 
6.6 
4.0 
4.0 
5.5 


Feet. 
9.0 
21.7 
8.8 
8.3 
4.5 
20.5 


Feet. 
3.2 

17.9 
2.2 
4.3 
0.5 

15.0 


Feet. 


1901-2 




1902-3 

1903-4 -. 

1904-5 .': 


2. 2 
2. 2 
1.5 



ESOPUS CREEK AT KINGSTON, N. Y. 



This station was established July 5, 1901. It is located at the 
Washington Street Bridge, Kingston, N. Y. ; about 1 mile from the 
West Shore Railroad station. The measurements are made from the 
upstream side of a two-span highway bridge. The main span is about 
117 feet wide. There is also a short span of about 19 feet on the left- 
hand end for extreme high water. The drainage area above this sta- 
tion is 324 square miles. The bed of the stream consists of earth and 
loose rock and is permanent. At ordinary stages the channel is from 
90 to 110 feet wide at the' bridge, but it is wider above and below. 
Upstream the channel is straight for about 300 feet. It then deflects 
slightly to the right. Downstream the channel is fairly straight for 
700 or 800 feet. Rapids about 300 feet below affect the low-water 



WINTER RECORDS. 31 

How. Measurementacan be made by wading above the Ulster and 
Delaware Railroad bridge, aboul I mile upstream. The right bank is 
of earth, of medium height and slightly wooded; il is not subjeel to 
overflow except at very high stages. The left bank is of ordinary 
height, slightly wooded, and subjeel to overflow in high water. The 
conditions are such that the overflow can be readily estimated. 

Esopus Creek receives numerous small tributaries mostly small 
torrential streams which cause rapid fluctuations in the main 
streams. The stream channel is usually broad and shallow, the bed 
being covered with cobbles and small bowlders, until the vicinity of 
the gaging station is reached, when the slope is more gradual and the 
current less swift. At OhVebridge, about 20 miles above the station, 
there is a natural fall of about 22 feet that is increased to 28 feet by a 
timber dam on the crest of the ledge, and at Glenerie, where the West 
Shore Railroad crosses the Esopus, about 6 miles downstream, there 
is a cascade that has a fall of about 56 feet. The final descent to tide- 
water at Saugerties is made through a fall of 42 feet. 

There are no dams in the vicinity of the gaging station, and the 
channel is unobstructed except by small rapids which affect the low- 
water flow only. The extreme stages observed are as follows : 

Extreme stagt s obsi rvi </ on Esopus Creek at Kingston , N. Y . 



Gage 
height. 



Discharge. 



High water. 
Low water. 



Feet. 
2.5. 
3.7 



Extreme range. 



St cond-feet. 

23,400 

36 

23,364 



Esopus Creek in this vicinity usually freezes over about December 
1, though the entire stream is not closed up. Ice generally forms 
first along the shore below the bridge and gradually works upstream, 
the velocity being swifter on the upstream side. The stream here 
has a wide range during the frozen season, the gage heights ranging 
from about 5 feet to 17 or 18 feet. These freshets sometimes occur 
as often as twice a month, and occasionally clear the creek of ice, this 
depending somewhat on the time of year and the thickness of the ice. 
The channel below the bridge sometimes becomes jammed, and in the 
spring it frequently has to be cleared out with dynamite. There is 
more or less open channel during the greater part of the winter at 
this station. Several ice measurements have been made here, and 
invariably there was a portion of the stream open. There are no 
reports or indications of needle ice, though it may form at times. 

During 1901, 1902, and 1903 there was comparatively little ice in 
this stream, but in the winter of 1904-5 the ice had a thickness of 



32 



STREAM FLOW DURING THE FROZEN SEASON. 



about 1.5 feet for a period of about six weeks, ranging from 0.1 to 0.2 
feet at other times. The ice went out about March 18. The range 
of winter gage heights and maximum thickness of ice observed are as 
follows : 



Range of winter gage heights and maximum thickness of ice on Esopus Creek at Kingston, 

N. Y. 



Date. 


Gage height to water surface. 


Maximum 

thicknes 

of ice. 


Minimum. 


Maximum. 


Range. 


1901-2 


Feet. 
5.28 
6.10 
4.91 
4.74 
5.35 


Feet. 
9.95 
'9. 82 
18.23 
12.90 
14.60 


Feet. 
4.67 
3.72 
13.32 
8.16 
9.25 


Feet. 
36 


1902-3 


43 


1903-4 


.80 


1904-5 


71 


1905-6 


1 42 







FISH RIVER AT WALLAGRASS, ME. 

This station was established July 29, 1903. It is located just 
below the outlet of Wallagrass Brook. The drainage area at this 
point is 910 square miles. Measurements of the flow are made from 
a cable located about 1,500 feet downstream from the gage, end 
soundings are made on the line of the cable. The bed consists of 
gravel and is permanent. The banks are of medium height, but 
rarely overflow during high stages. The channel is straight for 500 
feet above and 300 feet below the cable and is about 100 feet wide, 
being fairly uniform in cross-section near the station. Wallagrass 
Brook is the only stream of any considerable size entering Fish 
River in this vicinity. The gaging station is about 8 miles above the 
entrance of Fish'River into the St. John and about 2 miles upstream 
from an undeveloped fall of about 20 feet. There are no dams in this 
vicinity. The extreme stages observed are as follows : 

Extreme stages observed on Fish River at Wallagrass, Me. 



High water 

Low water 

Extreme range 



Gage 
height. 



Feet. 
13. <i 
1.7 



Discharge. 



Second-feet. 

8,300 

50 



8,250 



Fish River in this vicinity usually becomes frozen over about 
December 1 and remains so without interruption until about April 1. 
Ice forms first at the shores and gradually extends across the stream, 
with the exception that in the vicinity of the gage a small area 
remains open for a time. Occasionally during the winter the ice 
thins out, owing to the entrance of water from springs. Winter 
freshets are unusual in this vicinity. Winter conditions are very 
uniform, fluctuations in stage are usually slow, and the ice cover is. 



WINTEB RECORDS. 



33 



smooth and permanent, so thai in general this station is especially 
favorable for records. The range of winter gage heights and maxi- 
mum thickness of ice observed arc as follows: 

Rangi of winter gage heights and maximum thickness qfia on Fish River at Wallagrass, Me. 





Date. 


i lage height to w ater surface. 


Maximum 

i tiickness 

of ice. 




Minimum. 


Maximum. 


R mge 




Feet. 
2. 8 
3. 3 

2.0 


Feet. 

5.0 
5. 2 
5.2 


Feet. 
2.2 
1.9 
3. 2 




[903 i 


Feet. 


1904 .". 


1.9 


L905 6 


1.5 







KENNEBEC RIVER AT NORTH ANSQN, ME. 

This station was established October IS, 1901. It is located Ih 
miles east of North Anson village and a short distance above the 
month of Carrabassett River. The drainage area at this point is 
2,880 square miles. Measurements are ordinarily made from the 
covered wooden highway bridge, known locally as Patterson Bridge. 

The bed of the stream is rocky, with stone and gravel in places, and 
is permanent. The right bank is high. The left bank is of medium 
height and is subject to overflow in times of highest water. At the 
bridge the channel is about 350 feet wide, broken by one pier. It is 
straight for about 100 feet upstream and 200 feet downstream from 
the bridge and is curved beyond these points. The channel widens 
out to about 500 feet a short distance up and down stream from the 
bridge. 

Carrabassett River enters the Kennebec about 1 mile below Pat- 
terson Bridge, and at its month is a large island dividing the Kennebec 
into two narrow channels. The nearest dam is at Madison, 6 or 7 
miles downstream, and backwater from this dam extends about to the 
mouth of Carrabassett River. Upstream the nearest dam is at Solon, 
about 8 miles above; the slope of the river in this portion at ordinary 
stages is in general about 4 feet to the mile, althougn it is concentrated 
somewhat at several points. At low water the velocity at the bridge 
becomes somewhat low and poorly distributed, and measurements 
have been made by means of a boat at a distance of about 1,000 feet 
downstream. The extreme stages observed are as follows: 

Extreme stages observed on Kennebec River at North Anson, Me. 



High water 

Low water 

Extreme range 



Gage 
height. 



Feet. 
14.95 
1.55 



Discharge. 



Second-feet. 
39,000 



38, 200 



irr 187—07- 



34 



STREAM FLOW DURING THE FROZEN SEASON. 



Kennebec River in this vicinity usually becomes frozen over during 
the first week in December and remains so without interruption until 
about March 15 or April 15. Near the bridge ice first forms at the 
shores and around the piers and gradually extends, the channel being 
completely frozen over in a week or so in ordinary seasons. During 
the winter of 1905-6, however, narrow channels remained open in 
each span until about January 1, and narrow areas of open water 
remained somewhat after this date for short distances above and 
below the bridge. 

In December there is probably considerable needle and anchor ice 
in the vicinity of the station, but after the ice becomes permanent no 
trouble has been occasioned from this source. 

Ordinary winter conditions are good for recording gage heights at 
this station. The range of winter gage heights and maximum thick- 
ness of ice observed are as follows: 

Range of winter gage heights and maximum thickness of ice on Kennebec River at North 

Anson, Me. 





Gage height to water surface. 


Maximum 

thickness 

of ice. 




Minimum. 


Maximum. 


Range. 


903-4 


Feet. 
2.3 
3.8 
3.4 


Feet. 
4.8 
6.6 
5.8 


Feet. 
2.5 

2.8 
2.4 


Feet. 

2.8 


904-5 


2.7 


90.5-6 


2.0 







RONDOUT CREEK AT ROSENDALE, N. Y. 

This station was established July 6, 1901. It is located at the high- 
way bridge in Rosendale about one-half mile downstream from the 
Wallkill Valley Railroad station. The drainage area above this point 
is 380 square miles. There is some diversion through the Delaware and 
Hudson Company's canal, which is parallel to the river and is oper- 
ated during the summer months from High Falls to tide water in Hud- 
son River at the mouth of Rondout Creek. This canal receives its 
supply from Rondout Creek at High Falls, 3 miles upstream from 
Rosendale, but a large percentage of this diversion returns before 
reaching the gaging station. Observations made at Creeklocks of 
the stage of water in the canal and a record of the number of lockages 
afford sufficient data to estimate the flow through the canal. As the 
canal is closed during the winter months, it has no effect on the 
winter's record. 

At the gaging station the bed of the stream consists of rock and is 
permanent. The channel at the bridge ranges from 90 to 135 feet in 
width and widens out considerably both above and below the bridge. 
It is straight for several hundred feet each way from the bridge, and 
some rifts about 1,000 feet downstream cause slack water at low 



WINTKR RKCORDS. 



35 



stages, when measurements are made at a ford about I mile below. 
Both hanks arc high and rocky and are not subject to overflow. 
Water passes under the bridge at all stages. 

There is practically 75 feel fall from the diversion dam near High 
Falls, about 3 miles above the station, to the junction with Wallkill 
River, about 3 miles below. There are no streams of importance 
Bowing into Rondout Creek in the neighborhood of Rosendale. The 
extreme stages observed are as follows: 

Extreme stages observed on Rondout Creek at Rosendale, N . Y. 



1 1 iirli water 

Low water 

Extreme range 



Gage 
height. 



Feet. 
19.40 
6.00 



Discharge. 



Second-feet. 

18,130 

50 



18,080 



Rondout Creek usually freezes over about December 1 and the ice 
goes out about March 1 . There are usually two or three freshets dur- 
ing this period that break the ice up and in most cases carry it out. 

The record was discontinued November 7, 1903, but started again 
about December 1, 1905, by the city of New York. The 1905-6 rec- 
ords show that the river was not closed by ice until about February 3 
and that the ice went out February 22. The range of winter gage 
heights and maximum thickness of ice observed are as follows: 

Range of winter gage heights and maximum thickness of ice on Rondout Creek at Rosendale, 

N. Y. 





Date. 


Gage height to water 


surface. 


Maximum 

thickness 

of ice. 




Minimum. 


Maximum. 


Range. 


1901-2 

1902-3 * 


Feet. 
6.95 
6.95 
5 04 


Feet. 
9.35 
9.85 
5.60 


Feet. 
2.40 
3.10 
.56 


Feet. 
0.42 
.40 


1905-6 


i 


.46 



WALLKILL RIVER AT NEWPALTZ, N. Y. 

This station was established July 7, 1901, and was discontinued 
November 19, 1903. It was located at the highway bridge in New- 
paltz, near the Wallkill Valley Railroad. The drainage area above 
this point is 736 square miles. The measurements were made from 
the downstream side of the highway bridge at all times except during 
extreme high water, when the Wallkill Valley Railroad bridge about 
3 miles below was used. At low stages the water is rather slack and 
it is difficult to obtain a satisfactory measurement. The bed of the 
stream is composed of clay with large cobblestones and some bowlders, 



36 STREAM FLOW DURING THE FROZEN SEASON. 

and is permanent. Upstream the channel is straight for 400 or 500 
feet; it then bends rather sharply to the right; downstream it is 
straight for several hundred feet. The right bank is rather high and 
slightly wooded, and does not overflow. The left bank is of medium 
height and is subject to overflow during high-water stages. 

The principal tributary to the Wallkill in the vicinity of Newpaltz 
is the Shawangunk Kill, which enters near Gardiner, about 7 miles 
above, its total drainage area being 149 square miles. The dam 
nearest the station is at Walden, about 12 miles above. At low 
stages slight rapids about 300 feet below the bridge cause slack water 
in places and affect the discharge ; at extreme high water a plain on 
the left side is overflowed, making it impossible to determine the 
flow at this point. The extreme stages observed were as follows: 

Extreme stages observed on Wallkill River at Newpaltz, N. Y. 



High water. 
Low water. 



Extreme range. 



height. 



Feet. 
24.8 
5.5 



Discharge. 



Second-feet. 

24,480 

105 



While Wallkill River freezes more or less in December, there are 
no records that show the stream to be completely closed before Janu- 
ary, and then only for short periods. Several discharge measure- 
ments under ice cover have been made, some showing backwater 
from ice and others giving fairly good results. In general, however, 
the river is partially open during the entire winter season, except in 
parts of January and February. The ice usually goes out about 
March 5. 

Ice records on Wallkill River at Newpaltz, N. Y. 

1902. 
January 12, ice 1.2 feet thick. 
January 19, ice 1.2 feet thick. 
January 26, ice 1.2 feet thick. 
February 2, ice 1.3 feet thick. 
March 1, high water. 

1903. 
December 11, 1902, to January 4, ice about 0.5 foot thick. 
January 4-17, ice 0.83 foot thick. 
January 18-24, ice 0.92 foot thick. 
January 25-31, ice 0.83 foot thick. 
February 1-26, ice 1 foot thick. 
February 28, ice went out under bridge. 
March 1-4, ice 200 feet above and 300 feet below bridge. 
March 5, river clear. 



WINTKK RECORDS. 



37 



The range of winter gage heights and maximum thickness of i<-<> 
observed are as follows: 

Range of winter i/<i<i< heights and maximum thickness ofia on WaUhUl River <// Newpaltz, 

X. )". 



half. 


Gage heighl to water surface. 


M:l xillllllll 

1 liickiicss 

Ol ire. 


Minimum. 


Maximum. 


Range. 


1901-2 


Feet. 

7. I'd 
7. 05 


Feet. 

is.:,!) 
16.55 


Fe( t. 
LI. 30 

9.50 


Feet. 

L.2S 


1902 -;; 


.82 







WINOOSKI RIVER AT RICHMOND, VT. 

This station was established June 25, 1903. It is located at the 
steel highway bridge about one-fourth mile from Richmond railway 
station on the road to Huntington. The drainage area at this point 
is 885 square miles. The bed consists of sand and gravel and is fairly 
permanent. The banks are fairly high, but overflow at extreme high 
water. The channel is slightly curved upstream, but straight for 
1,000 feet or more downstream. It is about 175 feet wide at the 
bridge, and somewhat wider above and below. The nearest dam 
downstream is at Essex Junction, about 8 or 9 miles below the sta- 
tion, and there is a considerable amount of undeveloped fall between 
these two points. Upstream the nearest dam is at Bolton Falls, 
about 7 or 8 miles above the station. The extreme stages observed 
are as follows : 

Extreme stages observed on Winooski River at Richmond, Vt. 



High water 

Low water 

Extreme range 



height. 



Feet. 
IS. 7 
3.7 



15.0 



Discharge. 



Second-feet. 

! 19,000 

139 



+ 18.8K1 



Winooski River in this vicinity usually freezes during the first part 
of December and remains frozen until about March 15. That part 
adjacent to and below the bridge, where the velocity is medium, 
freezes first. About one-fourth mile upstream, where a stretch of 
quick water begins, freezing takes place considerably later, and dur- 
ing some winters a permanent ice cover does not form here. 

The contraction in the channel at the bridge tends to cause ice 
jams, and low velocity just below favors the formation of thick ice. 
During the January freshet of 1906 a jam affected gage readings dur- 
ing the remainder of the winter season. PI. I, B (p. 24), shows the con- 
ditions at the gaging section March 9, 1906. The ice is extremely 



38 



STEEAM FLOW DURING THE FROZEN SEASON. 



rough, broken, and tilted, and the gage heights give no index what- 
ever of the flow, which was confined to about one-third the ordinary 
width of channel. The range of winter gage heights and maximum 
thickness of ice observed are as follows: 

Range of winter gage heights and maximum thickness of ice on Winooski River at 

Richmond, Vt. 





Gage height to water surface. 


Maximum 

thickness 

of ice. 




Minimum. 


Maximum. 


Range. 


1903-4 


Feet. 
4.15 
4.95 
4.9 


Feet. 
6.7 
5.7 
14.7 


Feet. 
3.55 

.75 
9.8 


Feet. 
2.75 


1904-5 '. 


3.05 


1905-6 : 


-fc2.5 







Ordinary winter -conditions are rather poor for estimates of flow at 
this station owing to the liability of unstable conditions. During 
low stages, which frequently occur in winter, the change in discharge 
is considerable for a slight difference in stage, and a slight change in 
the controlling ice conditions downstream may markedly affect the 
discharge : 



GAGE HEIGHTS AND DISCHARGE MEASUREMENTS. 

The following measurements have been made at the stations 
described above. 

Stream measurements during frozen season. 
CATSKILL CREEK AT SOUTH CAIRO, N. Y. 













Gage 

height- 






Gage height 


Gage height 












o5 
o 




to water 
surface. 


to bottom 
of ice. 




's 

o 

03 


o5 
.2 


O a) 


ft" 


O 05 


A fl * 

, ft 


Date. 




o 


>> 




P 




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Sec- 




1901 


Feet. 


Sq.ft. 


sec. 


feet. 


Feet. 


Feet. 


Feet. 


Feet. 


feet. 




feet. 




December 9 


a 65 


106 


1.03 


110 


3.30 


2.93 


0.37 




120 


0.92 


66 


1.67 


1902 


























January 15 


90 


166 


.89 


148 


3.50 


2.84 


.66 




152 


.97 


53 


2.79 


1906 


























February 16 


100 


190 


.33 


62 


2.82 


2.22 


.70 




56 


1.11 


17 


3.65 



a Gaging made 70 yards below bridge. 



GAGE HEIGHTS AND DISCHARGE MEASUREMENTS. 
Stream measurements during frozen season Continued. 

CONNECTICUT RIVER AT ORFORD, \ II 



I 'HI.'!. 

January 24 . 
January 29 . 
January 29 . 
ranuary 30 . 
February 7. 
February ~ . 

1901. 
February 3. 
February 3. 
February 4 . 
February 4. 
February 5. 
February 5 . 



1905. 
February 2S. 

March 1 

March 1 



1906. 
February 8 . . 
February 15. 
February 17. 
March 14. 
March 15 



Feet. 
276 

273 
27.', 
276 
278 
278 



Qj 


>, 






U 








•a 




5 


> 


03 


§ 






< 


a 




Feet 




■per 


Sq. It. 


sec. 


1,7611 


1.69 


1.6111 


1 . 63 



327 
327 
327 
327 
327 




RSOPUS CREEK AT KINGSTON, N. Y. 



1901. 
December 4.. 

1902. 
January 9 " . . 
February 28 << 
Decern ber 11 . 
December 1 c. 

1903. 
January 14 d. 
February 24 « 

1906. 

February 15 . 



100 
116 
90 
116.6 



101.6 
104.6 



419 

706 

404 

1,170 



413 
443 



1.25 
2.39 
1.18 
2.96 



1.03 
1.47 



236 



522 
1,690 

476 
3, 460 



250 



6.54 
9.14 
1.60 
13 



425 6.9 
654 7. 1 



5.60 



6.41 
8.94 
6.50 



6.32 
6.70 



.13 
.20 

.10 



.58 
.40 



716 
2, 030 

741 
5,300 



Mi! 
950 



.73 
.83 
.64 
.65 



.49 
.69 



669 

1,900 
700 



638 
782 



.67 

.84 



.83 



FISH RIVER AT WALLAGRASS ME. 



1906. 
February 15 

Do .... . 
March 15 | 115 

Do 



9.5 


205 


0.95 


195 


3.91 


2.66 


1.25 


0.65 


620 


0.32 


225 


95 


205 


.96 


196 


3.91 


2.66 


1.25 


.65 


620 


.32 


225 


115 


312 


1.21 


378 


4.99 


3.83 


1.20 


.9 


1,080 


.35 


580 


115 


319 


1.22 


390 


5.08 


3.92 


1.20 


.9 


1,125 


.35 


620 



0.87 
.87 
.65 
.63 



a Partly frozen over: stations 20-70 and 110-115 open. 
b Partly frozen over: stat : ons 0-25 and 110-116 open. 

c River frozen over 150 feet below bridge and 200 feet above. Measurements taken at 0.6 depth. Ni 
ice at bridge. 
d Stations 15-40 river open. 
« Stations 12-40 river open; ice rough. 

Note.— February 8 and 17. river partly open for a short distance below bridge. March 14 and IS 
river partly open for a short distance below bridge, but not as much as on February 17. 



40 



STKEAM FLOW DUEING THE FROZEN SEASON. 



Stream, measurements during frozen season — Continued. 

KENNEBEC RIVER AT- NORTH ANSON, ME. 



Date. 



height- 



Gage height 
. to water 
surface. 



— o CJ 

A 



OoO« 

CgojC 

o 



Gage height 

to bottom 

of ice. 



i£ a 



1904. 
January 27 . 
January 28 . 

March 2 

March 4. . . . 

1905. 
February 9. 
Do.;... 

1906. 
January 9». 
January 10 a 

March 2 

March 3 

March 30... 

Do 

Apr 111''... 

Do. &.... 



Feet. 
240 
240 
230 
230 



458 
45S 



440 
440 
445 
445 
447 
447 
450 
450 



Sq.ft. 
393 
398 
285 

285 



1,390 
1,390 



1,100 
1,030 
1,140 
1,050 
1,180 
1,200 
1,210 
1,240 



Feet 
per 
sec. 
1.90 
1.97 
1.86 
2.01 



1.50 
1.54 



1.17 
1.09 
1.40 
1.31 
1.36 
1.38 
1.37 
1.38 



Sec- 
feet. 
749 
786 
529 
572 



2, (ISO 
2,140 



1,290 
1,120 
1,590 
1,380 
1,600 
1,660 
1,660 
1,710 



Feet. 
3.40 
3.40 
3.55 
3.65 



5.27 
5. 32 



3.58 
3.40 
4.26 
4.08 
4.77 
4.80 
4.70 
4.70 



Feet. 
1.55 
1.55 
1.45 
1.55 



3.27 
3.32 



2.38 
2.22 
2.43 
2.27 
2.67 
2.70 
2.80 



Feet. 
1.8 

1.8 
2.1 
2.1 



2.10 
2.10 



1.28 
1.30 
1.97 
1.98 
2.26 
2.26 
1.95 
1.95 



Feet. 
2.0 
2.0 



1.0 
1.0 



.1 
.1 
.1 
.1 
.0 
.0 
±1.0 
±1.0 



Sec- 
feet. 
3,170 
3,170 
3, 450 
3,650 



7,530 
.7,680 



3,520 
3,170 
4,980 
4, 580 
6,220 
6, 300 
6,050 
6,050 



0.24 
.25 
.15 
.16 



.28 
.28 



.37 
.35 
.32 
.30 
.26 
.26 
.28 
.28 



Sec- 
feet. 

±675 
±675 
±600 
±675 



2,920 
3,020 



1,550 
1,370 
1,630 
1,420 
1,950 
1,990 
2,140 
2,140 



RONDOUT CREEK AT ROSENDALE, N. Y. 



1901. 
December 6 « 

1902. 

January 14. . 

February 8. 

February 26. 

Do.".... 

1903. 

February 25 . 

1Q06. 

February 27. 



105 
102 
80 
100 

115 

117 



479 
732 
489 
517 

474 

555 



1.62 
1.11 
1.32 



1.6 
.35 



423 
732 
543 
684 



676 
194 



7.00 
8.81 
8.13 
8.43 



7.9 
eb. 15 



6.53 
8.41 
6.71 
7.01 



7.40 
4.51 



.47 

.40 

1.42 

dl.42 



.50 
.46 



540 
2,330 
1,610 
1,930 



4, 370 



.78 
.31 
.34 
.35 



247 

1,900 

359 

549 



WALLKILL RIVER AT NEWPALTZ, N. Y. 



1901. 
December 11 /. 

1902. 

January 21 

January 23 9 . . 
January 31ft. . 
February 10 . . 
February 24.. 

1903. 
February 7.. . 
February 10 L 
February 26. . . 



Mil 
1(10 
115 
85 



140 
142 
130 



679 
496 



1,070 
999 
757 



.78 
3.22 
1.72 
1.20 

.74 



2.14 
2.03 
1.24 



3,040 



332 

6,060 

1,170 

597 

288 



2, 290 

2,030 

945 



7.24 
17.33 
9.07 
7.78 
7.35 



11.2 
10.9 
8.85 



6.04 
16.41 
8.07 
6.78 
*5. 25 



10.45 
9.73 
7.89 



1.20 
.92 
1.00 
1.00 
2.10 



.75 
1.17 



860 
9,290 
1,980 
1,160 

919 



3,580 
3,330 
1,830 



3,250 



277 
8,300 
1,330 

619 



2,970 
2,440 
1,230 



a Frozen except for narrow channels above and. below bridge. 
6 Frozen except for narrow channel near left bank. 

c Ice varied from one-half inch to 5 inches from bank to bank at riff just below; ice extended one-third 
way across. 
d Estimated from previous measurements, same date, 
e Subject to correction. 
/ Ice cover from stations 40-85. 
g Ice badly broken at station 20. 
ft Ice badly broken at station 110. 

i Below rating table; water considerably above top of ice. 
i Stations 135-142 open. 



GAGE HEIGHTS AND DISCHARGE MEASUREMENTS. 

Stream measurements during frozen season Continued. 
WINOOSK1 RIVER \T RI< BMOND, VT. 



41 













Gage 
height 






Gage height 


Gage heighl 
















to water 
surface. 


in iini torn 
of ice. 




31 




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Date. 




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1905. 


Fret. 


Sq.ft. 


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feet. 


Feet. 


Feet. 


Feet. 


Feet. 


feet. 




feet. 




March 3 


75 
75 


it*** 

114 


1.89 
2. 30 


206 

262 


5.45 
5. 58 


2.70 
2. 83 


2.95 
2. 95 






1,460 
1,610 


0. 14 
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March i 






1906. 








70 


348 


1.68 


585 


5.62 


±3.4 


±2.8 





1,650 


.35 













a Channel open 1,000 feet upstream and one-half mile downstream. Ice very rough, broken, and 
tilted, reaching to bottom for about two-thirds of section. 

The follewing table includes some single sets of discharge meas- 
urements, with a brief description of the conditions. As a rule, 
these are insufficient in range at a given station to give much infor- 
mation regarding the winter rating curve. 



42 



STREAM FLOW DURING THE FROZEN SEASON. 



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WINTKK RECORDS. 



43 



STATION RATING CURVES FOR ICE COVER. 
GENERAL CONSIDERATIONS. 

At several stations sufficient data Lave been gathered to con- 
struct a rating curve for conditions of ice cover, applicable to aver- 
age ice conditions within the range of winter gage heights, hut the 
variation in form of curve with change in thickness of ice is still 
uncertain, and the proper rating curve or coefficient to apply for the 
time when the ice is thin has not been sufficiently verified by gagings. 
A station rating curve for conditions of ice cover must evidently be 
constructed on one of the following bases: (1) Gage heights to the 
surface of the water as determined from a hole cut in the ice, or 
2) gage heights to the bottom of the ice. 




N VELOCITY - FT PER SEC. 

Fig. 4.— Rating and velocity curves under ice cover, Wallkill River at Newpaltz, N. Y. 

In figs. 4 to 6 are shown the results of such gagings as have been 
made under ice cover at three gaging stations, the gage heights being 
plotted in each of the above ways and the open-water rating curve 
being shown for comparison. 



WALLKILL RIVER AT NEWPALTZ, N. Y. 

So far as can be determined at present, the rating curve based on 
gage heights to the water surface seems to give the best results; 
that is, the points lie more nearly on a smooth curve (fig. 4). There is 
no great difference, however, except in the case of the lowest gag- 
ing, in which the thickness of the ice was perhaps only half of the 



44 



STREAM FLOW DURING THE FROZEN SEASON. 



distance, 2.1 feet, from the water surface to the bottom of the ice, 
indicating that the water below the ice was under some pressure. 
It will be noticed that the range in ice thickness is not large. 




3000 4-000 5000 6000 

CU. FT. PER SEC. 

1904 DISCHARGE MEASUREMENTS = O 

1905 " " = 9 

1906 " " = • • 

FIGURES DENOTE DISTANCE FROM WATER SURFACE TO BOTTOM OF1CT. 

Fig. 5.— Rating curve under ice cover, Kennebec River at North Anson Me. 
KENNEBEC RIVER AT NORTH ANSON, ME. 

The effect of varying thickness of ice on discharge for a given gage 
height is clearly shown (fig. 5) . No one curve can be drawn through the 
points plotted for the gage heights to the water surface, although a few 



STATION RATING 0URVE8. 



45 



more gagings would, perhaps, enable a scries of curves to be drawn 
for different distances from the water surface to the bottom of the 
ice. It is preferable to use these distances rather than thickness of 
the ice, for the position of the bottom of the ice with reference to 
the water surface is not only dependent on the ice thickness (in 
general being about 92 per cent of it), but will also vary with the 




2000 3000 4000 

DISCHARGE-CU. FT. PER SEC. 



5000 



6000 



1903 DISCHARGE MEASUREMENTS = © 

1904 " " = O 

1905 " " = O 

1906 " " = • 
FIGURES 0ENOTE DISTANCE FROM WATER SURFACE TO BOTTOM OF ICE 

Fig. 6.— Rating curve under ice cover, Connecticut River at Orford, N. H. 

snow load and thus include its effect. If gage heights to the bot- 
tom of the ice are used a fairly consistent curve is obtained for this 
station. 

CONNECTICUT RIVER AT ORFORD, N. H. 

The same general results appear here as in the case of the Ken- 
nebec, although the range of ice thickness is less (fig. 6) . The gagings of 
1903 and 1904 are open to some question, owing to the manner in 



46 STREAM FLOW DURING THE FROZEN SEASON. 

which they were made, and have been given little weight in draw- 
ing the curve as shown. 

GENERAL FORM OF RATING CURVE FOR ICE COVER. 

The curve, as constructed with gage heights to the bottom of the 
ice, in general lies to the left of the open-water rating curve, but 
tends to approach it in its lower portion and perhaps to cross it. 

The degree of curvature of the two curves is in general about the 
same in their lower parts and, like the open-water curve, the rating 
curve for ice cover is apparently a tangent in its upper part. In 
fact, it will be noticed in the case of the Wallkill and Connecticut 
that the ice-cover curve will be approximately the same as the open- 
water curve if the latter is swung around the intersection point of 
the two curves until the upper parts coincide. 

With gage heights to the surface of the water, the indications are 
that the curve for ice cover (or rather the series of curves con- 
structed for different thicknesses of ice) will be approximately par- 
allel to the curve determined by gage heights to the bottom of the ice. 

RELATION BETWEEN DISCHARGE UNDER ICE COVER AND FOR OPEN 

SECTION. 

If gage heights are taken to the bottom of the ice and the dis- 
charge compared with that for the same gage heights in open chan- 
nel, it is found that as the stage increases this ratio decreases. In 
the case of the Wallkill, this ratio is greater than unity below about 
gage height 6.8, where the curves cross, and decreases from this point 
to a value of about 0.71 at gage height 18.0. With the Connecticut 
the range in this ratio is from 0.97 at gage height 2.0 to 0.78 at gage 
height 6.0. Evidently no mean value of the ratio can be assumed 
that will give anything more than rough results. 

It is not deemed wise in the light of existing data to advise the use 
of either one of the above-described methods for the construction of 
rating curves to the exclusion of the other, although the indication 
seems to be that the use of gage heights to the bottom of the ice will 
prove most generally convenient. There will undoubtedly be cases, 
however, where this method must be used with caution, more espe- 
cially in the lower part of the curve, as it would not take into account 
the effect of ice being held down by shores or piers, and the conse- 
quent pressure or head under which flow was taking place. 

VERTICAL VELOCITY MEASUREMENTS UNDER ICE COVER. 
DETAILS OF VERTICAL VELOCITY CURVES. 

The principal data for vertical velocity curves at 25 stations are 
given on the following pages. It will be noted that each curve can 
be replotted from the table, if desired. In general, mean results 
are given for each set of curves taken, but some sets are subdivided 
in order to separate different conditions. 



VERTICAL VELOCITY CURVES. 



47 



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VERTICAL VELOCITY CURVES. 



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72 STREAM FLOW DURING THE FROZEN SEASON. 

SUMMARIES OF VERTICAL VELOCITY CURVES. 

The mean results from the vertical velocity curves (pp. 47-71) 
have been arranged in three groups — (1) 352 curves for smooth ice 
cover, (2) 51 curves for rough ice cover, (3) 13 curves for very rough 
ice cover. It will be noted that in some cases where gage heights 
were approximately the same for different sets of curves they have 
been combined. There is little difference between the results of 
groups 1 and 2, but as rough ice cover was reported for group 2, it 
seemed best not to include it in the larger list. 



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VERTICAL VELOCITY iri:\ i:s. 



75 



FORM OF VERTICAL VELOCITY CURVE. 

For an ideal cross section and Length of river, the difference in 
velocity at different points in a vertical section is due to the differ- 
ence in resistance to flow met with by the filaments of water at 
different depths. If no resistances of any kind existed, the vertical 
curve of velocity would be a straight line normal to the surface of 
the stream. If bed friction and the incidental losses due to it were 
the only resistances to flow, the vertical velocity curve would prob- 
ably be curved in the lower part and straight in the upper part, the 
line being tangent to the curve at that point in the vertical where the 
effect of bed resistance is lost (fig. 7, a) ; or if the bed friction is of 
sufficient amount relatively to the depth the curve might be continu- 
ous to the surface (fig. 7, b). Varying degrees between a and b 
would be met with, depending on the relation of depth to velocity, 
condition of bed, etc. If there is resistance at the surface due to air 
friction only, there would be a similar effect on the form of the curve 



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Fig. 7. — Form of vertical velocity curves. 



from the surface downward. If there were no bed friction, the form 
of curve would be as in fig. 7, c, or some modification of this, as 
explained above. 

Resistance to flow occasioned by the roughness of the sides of a 
stream is also an important factor in determining the form of the ver- 
tical velocity curve, especially if the channel is narrow and deep. 
F. P. Stearns a has advanced the theory that there is an upward flow 
toward the center at the surface. He says: 

Let us first suppose the case of a single obstacle projecting from the lining of a channel. 
The current approaching this obstacle loses some of its velocity just before reaching it, and 
thereby causes an excess of head in a small pyramid of water just above the projection. 

This excess of head in turn causes a transverse flow of the water in all directions ; but the 
strongest transverse flow will be in the direction of the least resistance, which is, as a rule, 
vertically toward the surface. 



a Trans. Am. Soc. Civil Eng., vol. 12, 1S83, pp. 331 et seq. 



76 STREAM FLOW DURING THE FROZEN SEASON. 

The irregularities upon the surfaces of even the smoothest channel linings met within 
practice are very large in comparison with the size of the particles of water striking them, 
and they may be considered as obstacles present in all parts of the lining, each tending to 
produce an upward flow, as above indicated. 

Although the tendency to upward flow is general, yet since it can not occur without a 
corresponding downward flow to replace the water which rises it follows that it will take 
place only in those portions of the width of the channel where the obstacles producing it are 
the more frequent and nearer the surface — i. e., generally at or near the sides. 

It is therefore the theory that there is at the sides of channels an upward flow, due to the 
cause already described, which carries with it the slow-moving water always found in the 
immediate vicinity of channel linings, and that this water, reaching the surface, flows 
toward the middle of the channel, retarding by its slower movement the velocity of the sur- 
face layers, thereby causing the maximum velocity to be, in most cases, below the 'surface. 

It must not be inferred from what has just been stated that the writer believes there is a 
continuous flow in the direction indicated, since it is well known that the motions of water 
are very irregular, particularly in channels with rough linings or variable sections, and that 
masses of water find their way from the bottom to the surface in the middle of the channel 
as wefl as elsewhere. The idea which he wishes to convey is that in most cases the resultants 
of these irra^ular movements are in the directions indicated. 

The typical vertical velocity curve for open-water conditions (fig. 7,d) 
may be considered as due to a combination of these various resist- 
ances,but the amount and direction of the wind may change greatly 
the retardation due to air friction, and consequently the form of the 
curv*e. The relative effect of bed and surface friction will be in a 
measure shown by the difference in length of mn and or, or, in other 
words, the relation of surface and bottom velocities to the maximum 
velocity. If there is an ice cover the upper part of the vertical veloc- 
ity curve will be still more curved (fig. 7, e), and, as shown later (pp. 
78-79) , may even be more pronounced in this way than the lower part. 

The foregoing statements would apply to a straight stretch of river 
with the bed approximately parallel to the water surface. The usual 
uneven conditions of bed and banks have a modifying influence and 
tend to obscure more or less the relative effect of bed and surface 
friction. This relation of top and bottom velocity to the maximum 
will, however, serve to indicate something of the relative amount of 
resistance due to ice cover and to the stream bed, and will be briefly 
considered. 

For open-water conditions the results from 78 vertical velocity 
curves under various conditions at gaging stations on New York 
streams are as follows : a 

Relation of top, maximum, and bottom velocity for open-water conditions. 





Velocity in 
terms of 

mean veloc- 
ity =1.00 


Difference 
as regards 
maximum 
velocity. 


Top ...: ; 


1.15 
1.18 
.50 


0.03 








.68 







"See Water-Sup. and Irr. Paper No. 76, U. S. Geol. Survey, 1903, p. 25. fig. 3. 



VERTICAL VELOCITY CURVES, 



77 



The relation of air or water surface friction to that of bed friction 
is here £;$§, or 0.044. (Compare with Francis's ratio of s ', „ for still 
air, p. L6.) 

For smooth ice cover, the comparative effect of bed and ice friction 
is shown for several cases in (he following table. The average amount 
of resistance due to ice cover is 0.58 of that due to roughness of bed, 
but there is considerable variation from this amount. 

Comparative <jf<<'t of bed mid ice friction <>// vertical velocity curves under smooth ia cover. 













Difference as re- 














gards maximum 




River and station. 


Cage 


Number 


\ \ erage 


Average 


velocity. 


Ratio hi' 


heignl . 


of curves 


depth. 


\ elocit v. 




1 to 2. 


















Top(l). 


Bottom 

(2). 












Feet ixr 










int. 




Feet. 


second. 








Kennebec, North Anson, Me... 


3.48 


is 


2.6 


1.17 


0.22 


0.62 


0.35 




4.17 


lit 


2.5 


1.30 


.30 


.112 


.48 




4.77 


9 


2.9 


1.33 


.40 


.57 


.71) 


Connecticut, Orford, X. II 


4.15 


IS 


4.0 


1.04 


.50 


.f,t; 


.76 




5.59 


/ 


4.6 


1.08 


.27 


.72 


.38 




(i.(K) 


7 


4.9 


1.11 


.32 


.72 


.44 




6.70 


21 


5.8 


1.23 


.41 


.(15 


.63 


Fish, Wallagrass, Me 


3.91 


8 


2.5 


.90 


.23 


.51 


.45 




5.04 


8 


3.6 


1.25 


.(14 


.74 


.86 






26 

5 


1.6 
8.0 


2.12 
2.18 


.59 

.37 


.65 




Wallkill. Newpaltz, X. Y 




.57 












.39 


.66 


.58 















For very rough ice cover, the frictional effect of ice cover is the 
greater of the two, averaging 1.28 times that for roughness of bed. 

Comparative effect of bed and ice friction on vertical velocity curves under very rough ice cover. 



River and .station. 



Number 
of curves 



Average 
depth. 



! Difference as re- 
gards maximum 
Average j velocity, 
velocity. 



Top(l). 



Bottom 

(2). 



Ratio of 
1 to 2. 



Rondout Creek, Rosendale, X. V 

Wallkill. Newpaltz, N. Y 

Winooski, Richmond, Yt 



Mean . 



Feet. 
5.3 
14.6 
6.2 



Feet yer 

second. 
0.74 
2.98 
1.99 



1.02 

.81 

1.11 



0.55 

.89 

1.05 

.83 



1.86 
.91 

1.96 

1.28 



RELATION OF DEPTH AND VELOCITY TO FORM OF CURVE. 



It is evident from the foregoing tables that for a given mean veloc- 
ity the vertical velocity curve under ice cover becomes flatter as the 
depth increases, since the curvature due to top and bottom resistances 
is distributed through a greater distance. (See fig. 13, p. 83.) For a 
given depth, as the mean velocity increases, the curvature will lie- 
come greater, as both top and bottom resistances increase with 
velocity. 



78 



STREAM FLOW DURING THE FROZEN SEASON. 



For a given station the change in curvature as the stage increases 
will depend on the relative increase of depth and velocity. In the 
case of Wallkill River (fig. 10) the depth increases considerably 
faster than the velocity, and it will be noted that the curve becomes 
natter as the stage increases. 



COMPAEISON OF VERTICAL VELOCITY CURVES, WITH AND WITHOUT 

ICE COVER. 

Fig. 8 affords a comparison of mean vertical velocity curves for 
conditions of open water and ice cover, at substantially the same 
stations. The essential difference between these curves is the greater 




o.zo 



0.40 
VELOCITY 



0.G0 0.60 1.00 

TERMS OF MEAN VELOCITY = 1.00 

Mean of 78 curves without ice cover 

Mean of 42 curves with ice cover 



Fig. 8. — Comparison of vertical velocity curves for streams with and without ice cover. 

drawing back of the curve for ice cover in its upper portion, on account 
of the greater retarding effect of the ice over that of air. As a conse- 
quence of tins there are two threads of mean velocity, viz, at 0.13 and 
0.71 of the depth, for ice cover, as compared to one mean thread at 
0.61 depth for the open section. The position of maximum velocity 
is lowered from about 0.14 depth in the case of open section to 0.36 
depth with ice cover, its relative value as regards mean velocity being 



VERTICAL VELOCITY 0URVE8. 



T'.i 



slightly less in the case of ice cover. The bottoms of the two curves 
arc at substantially the same position, as would be expected. 

With very rough ice cover the difference between the two curves 
becomes still more pronounced, and the drawing hack of the curve 
in its upper part may predominate over the curvature existing in 
the lower part due to roughness of bed. 



POSITION OF THREADS OF MEAN VELOCITY. 

The data in the tabic on pages 73-74 and figs. 8 to 14 serve as a 
basis for the following discussions, except where special reference 
is made to other material. 




0.20 



0.40 0.60 0.80 1.00 

VELOCITY IN TERMS OF MEAN VELOCITY = 1.00 



1.20 





GAGE 
HEIGHT 


NO. OF 
CURVES 


AVERUGE 
DEPTH 


AVERMjE 
VELOCITY 


Jan. 10, 1906 


3.48 


18 


2.6 


1.17 


Mar 2, 1906 


4.17 


19 


2.5 


1.30 


Mar 30, 1906 


417 


9 


2.9 


1.33 



Fig. 9. — Vertical velocity curvi 



: under ice cover, showing change in form of curve with change of stage, 
Kennebec River at North Anson, Me. 



The average of 352 vertical velocity curves made under widely 
varying conditions (pp. 73-74) indicates that in general under ice cover 
two threads of mean velocity occur in the vertical, their average 
position being at 0.10 and 0.71 of the depth below the bottom of 
the ice. 



80 



STREAM FLOW DURING THE FROZEN SEASON. 



The depths of threads of mean velocity being plotted as ordi- 
nates and the total depths as abscissas, it is seen that there is a 
general tendency for both threads to move toward the bottom of 
the curve as depth increases. A similar plat for depths of threads 
of mean velocity and for mean velocities indicates that as mean 
velocity increases both threads of mean velocity become lowered. 
An increase in stage for a given station means usually an increase 
of both depth and mean velocity; consequently it will be found 




0.40 0.60 0.80 1.00 1.20 

VELOCITY IN TERMS OF MEAN VELOCITY = 1.00 





&A&E 
HEIGHT 


AVERft&E 
DEPTH 


AVERAGE 
VELOCITY 


Jan. 21, 1902 


7 24 


6.7 


1.04 


Jan. 31, 1902 


9.01 


9.0 


2.16 


Jan. 23, I90E 


17.33 


21.3 


3.93 



Fig. 10.— Vertical velocity curves under ice cover; average of curves at stations 80, 90, 100 for different 
stages, Wallkill River at Newpaltz, N. Y. 

that both threads of mean velocity tend to move downward as the 
stage increases. (See figs. 9 to 11.) 

The range in position of mean threads seems to be about the 
same for both upper and lower threads, being about 0.18 depth 
(with a few exceptions). Moreover, the change in position of the 
two threads is about the same in amount, the average difference 
being 0.60 of the depth. With very rough ice cover the tendency 
is toward greater depression of both mean threads, but it will be 



VERTICAL VELOCITY 0URVE8. 



SI 



noted that they si ill preserve about the same distance apart, viz, 
0.60 depth. (See table on pp. 73-74, and fig. L4,p. 84). 

POSITION OF MAXIMUM VELOCITY AND RELATION TO MEAN VELOCITY. 

The average position of maximum velocity is at 0.37 depth below 
the ice, varying from 0.19 to 0.52 depth. In general, it becomes 




0.40 
VELOCITY 



0.60 0.80 1.00 

IN TERMS OF MEAN VELOCITY =1.00 



Feb. 1305 



6AGE 

HEIGHT 


NO OF 
CURVES 


AvERJkGE 
DEPTH 


AVERAGE 
VELOCITY 


4 15 


18 


4.0 


1.04 


6.10 


21 


5.8 


/.23 


6 00 


7 


4.9 


l.ll 


5.59 


7 


4.6 


I.0B 



Feb. 1906 

. . Mar/906 

Alar. 1906 

Fig. 11.— Vertical velocity curves under ice cover, showing change in form of curve with change of 
stage, Connecticut River at Orford, N. II. 

lower as the depth and velocity increase and hence as the stage 
increases. Rough ice cover tends also to lower the depth of the 
maximum thread, and when the ice becomes broken and tilted or 
when needle ice accumulates near its under surface the thread may 
be considerably below mid depth, indicating a greater effect due to 
ice friction than to that of the stream bed; in other words, the 
curve is a complete reversal of the ordinary open-water vertical 
velocity curve. 

ibb 187—07 6 



82 



STREAM FLOW DURING THE FROZEN SEASON. 



The average coefficient to apply for obtaining maximum from 
mean velocity is 0.839, the variation being from 0.76 to 0.90. This 
coefficient becomes less as the velocity increases, but greater as the 
depth increases, consequently its variation from the mean is not 
large for smooth ice. For rough ice it is considerably diminished 
and may reach a value of 0.75. 



RELATION OF VELOCITY AT MID DEPTH TO MEAN VELOCITY. 

The average coefficient for obtaining mean velocity from that at 
mid depth is 0.878, the range being from 0.82 to 0.92. The range 




0.40 0.60 0.90 1.00 

VELOCITY IN TERMS OF MEAN VELOCITY = 1.00 



Feb. 1906 



&A&E 

HEI&HT 


NO OF 
CURVES 


AVERAGE 
DEPTH 


AVERAGE 
VELOCITY 


3.31 
5 04 






2.5 
5.6 


0.90 
I.Z5 



Mar. 1906 

Fig. 12. — Vertical velocity curves under ice cover, Fish River at Wallagrass, Me. 

in values for this coefficient, like that for maximum velocity, is 
small, as the tendency is for it to increase directly with the depth 
and inversely with the velocity; consequently for a given station 
little variation occurs as the stage changes. Nearly this same aver- 
age relation was found on the upper Mississippi by A. O. Powell, 
assistant engineer, under the direction of Col. Charles J. Allen, Corps 
of Engineers, IT. S. Army, in 1882 and 1890,° the variation being 

a Ann. Rept. Chief of Engineers, U. S. A., 1890, pt. 3, p. 2104. 



VERTICAL VELOCITY CURVES. 



83 



between 0.87+ and 0.88 + . No data arc given, however, as to con- 
ditions of depth, velocity, or bed of stream. The coefficient for 
obtaining mean velocity from that at mid depth becomes less for 
very rough ice, just as in the case for maximum velocity, the aver- 
age value for the 13 curves being 0.82, with a range of from 0.76 
to 0.85. 

RELATION OF MEAN OF VELOCITIES AT 0.2 AND 0.8 DEPTH TO MEAN 

VELOCITY. 

The average coefficient for obtaining mean velocity from the mean 
of the velocities at 0.2 and 0.S depth is 1.002, the range being from 



r 




. 


^^^ > 


\ 












'VS. 

/A \ 

\ 

\ 
\ 
i 










-t 












/ t / 


/ / 
/ / 








^^''' 









020 



40 60 80 100 

VELOCITY l/N TERMS OF MEAN VELOCITY = 1.00 



Winooski River at Richmond Yt . 



8ED 


NO OF 

cuavts 


4VEH&&E 
DEPTH 


xvehh&e 
velocity 


Gravel 
Clay & Cobbles 


26 
S 


16 
8.0 


2.12 
2 Id 



Wall kill River at Nerrpaltz N Y 

Fig. 13.— Effect of depth on form of vertical velocity curves under ice cover. 

0.9S to 1.04, there being, however, but one set of curves with a 
greater value than 1.02. This relation is shown graphically by con- 
necting the 0.2 and 0.8 depth points of the mean vertical velocity 
curves and noting where this line crosses the horizontal at 0.5 depth. 
(See figs. 8 to 13.) 

In general, this coefficient seems to decrease slightly as gage 
heights increase. (See figs. 8 to 1 1 , and table on pp. 73-74.) For very 
rough ice cover the mean value is 1.002, the range being from 1.00 



84 



STREAM FLOW DURING THE FROZEN SEASON. 



to 1.04, indicating that rough ice tends to increase this coefficient 
slightly. 

The typical vertical velocity curve for open-water conditions cor- 
responds approximately in form with an ordinary parabola drawn 
through top, bottom, and mid-depth points of the curve and with 
axis horizontal. The mean ordinate to this parabola is a mean of 
the ordinates at 0.22 and 0.79 of the depth, and it is evident that 
the mean of the ordinates at 0.2 and 0.8 depth would always be 
less than the true mean ordinate, so that if the vertical velocity 



0.60 





^^ 


^ 


"v. 












^\^V. 


NS \ 












\ 

\> 

\ 

1 

1 


\ 










/ 
y 


J / 




_^ 


^-: 


<^ 







0.40 
VELOCITY 



0.60 80 100 

TERMS OF MEAN VELOCITY = 1.00 



Rondout Creek at Rosen dale, Al. Y. 
Wall hi 1 1 River at Mwpa/tz, N.Y. 
Winooski River at Richmond, Vt. 



BED 


NO. OF 
CURVES 


AVERAGE 
DEPTH 


AVERAGE 
VELOCITY 


Rook 
ClayS cobbles 
SandbgmYel 


4 

4 
5 


S3 

14.6 
6.2 


0.14 
2 99 

1.99 



Fig. 14.— Effect of very rough, broken, and tilted ice on form of vertical velocity curves under ice cover. 

curve were truly parabolic the coefficient for this method would 
always be slightly greater than 1.00. Usually the parabola passes 
wholly to one side of the actual curve above mid depth and on the 
opposite side below mid depth, the resulting effect being that the 
mean of the velocities at 0.2 and 0.8 depth ordinarily gives closely 
the mean velocity for the vertical. 

For ice cover the vertical velocity curve diverges markedly from 
a parabola drawn as described above. The results of the table on 
pages 73-74 seem to indicate, however, that this relation holds almost 



VERTICAL VELOCITY CURVES. 



85 



as well for Curves tinder ice cover as with open seel ion, and I he 
0.2 and 0.8 method, as it is called, seems to have much promise as 
a two-point method, being both reasonably accurate and convenient 
for use. 

The range of variation in the reduction of coefficients is as follows: 

Range of coefficient to reduce l<> mean velocity. 

Maximum 0. II 

10 

0(> 



Mid depth 

0.2 mid 0.8 deptli 

The accuracy of the method being assumed to be proportional to 
the square root of the number of observations, and either of the single- 
point methods being adopted as a basis, the computed probable range 
of error for the two-point method would be 
Range for single point 

or, as compared with maximum point, the range would be 0.099; with 
mid-depth point, the range would be 0.071. The actual range of 
variation for the two-point method is considerably smaller, indicating 
that it has a greater accuracy as compared with single-point methods 
than can be attributed to the use of two observations instead of one. 



PERCENTAGE VARIATION IN OBSERVATIONS AT DIFFERENT DEPTHS. 

In general the top and bottom of the vertical velocity curve is most 
poorly determined, because greater variations occur in velocity in 
these portions of the curve. The 0.5 depth method has the advantage 
of utilizing a depth of observation at which variations in velocity are 
least apt to occur. 

As bearing on the variations between successive observations at 0.2 
and 0.8 depth, the following table gives results from two sets of curves 
where independent observations were made at these depths just after 
the curves were completed : 

Variation in observations at 0.2 and 0.8 depth, Connecticut River at Orford, N. H., meter 

suspended from cable. 

MARCH 14, 1906, GAGE HEIGHT, 6.00. 



Average of 7 curves . 

Highest 

Lowest 



Observed velocity. 

Ratio: Velocity from 

curve. 



0.2 
depth. 



0.993 
1.07 

.94 



0.8 
depth. 



0.995 

1.05 

.95 



Ratio of velocity 
determined by 
the 0.2 and 0.8 
method to the 
mean velocity. 



Actual 
observa- 
tion. a 



1.013 
1.04 

.98 



From 
curve. & 



1.004 

1.02 

.99 



Depth 
under 



Feet. 
5.0 
6.3 
3.5 



Mean 
velocity. 



Feet ver 

second. 

1.10 

1.39 

.56 



a Mean from 0.2 and 0.8 velocity as observed. 

b Mean from 0.2 and 0.8 velocity taken from vertical velocity curve. 



86 



STREAM FLOW DURING THE FROZEN SEASON. 



Variation in observations at 0.2 and 0.8 depth, Connecticut River at Orford, N. H., meter 
suspended from cable — Continued . 

MARCH 15, 1906, GAGE HEIGHT 5.59. 





Observed velocity 

Ratio: Velocity from 

curve. 


Ratio of velocity 
determined by 
the 0.2 ahd 0.8 
method to the 
mean velocity. 


Depth 

under 

ice. 


Mean 
velocity. 




0.2 
depth. 


0.8 
depth. 


Actual 
observa- 
tion. 


From 
curve. 






1.006 

1.04 

.95 


0.974 

1.13 

.90 


1.011 
1.05 

.97 


1.003 

1.01 

.99 


Feet. 
4.6 
5.7 
3.2 


Feet per 
second. 
1.08 




1 36 




51 







As would be expected, the actual observations at 0.2 and 0.8 depth, 
when used to obtain mean velocity, give a larger percentage varia- 
tion in coefficient than do the curve values at these depths, but the 
average variation is small and far within the degree of accuracy 
required. 

A further index of the amount of variation in observations at 0.2 
and 0.8 depth is afforded by two successive gagings made February 
15, 1906, on Fish River at Wallagrass, Me., under ice cover, when the 
gage heights height remained the same. 

Comparison of velocities for two separate gagings on Fish River at Wallagrass, Me., gage 
height 3.91, meter fastened to rod. 

FEBRUARY 15, 1906, GAGE HEIGHT 3.91. 



Average of 4 stations, observations at 0.2 and 0.8 

depth 

Highest 

Lowest '. 

Average of 4 stations, vertical velocity curves 

Highest 

Lowest 



Ratio of velocities obtained 
in first and second gagings. 



0.2 
depth. 



1.002 

1.06 

.93 



0.8 
depth. 



0.972 

1.08 

.91 



Mean 



0.990 
1.05 

.94 
0.978 
1.01 

.95 



Depth. 



Feet. 
2.6 
4.1 
.9 
2.5 
3.6 
1.3 



Mean 
velocity. 



Feet per 

second. 

0.88 

1.10 

.62 

.90 

1.18 



Other details of these gagings are given on page 53. It will be noted 
that the depths are small and that in order to get 0.2 and 0.8 depth 
the meter had to be held within a range of 0.2 to 0.8 feet from the 
bottom of the ice and the bed of the river. The average variation in 
the results of these two sets of velocities at 0.2 and 0.8 depth is small 
and, in fact, is less than in the case of the vertical curves. 



STREAM l<' LOW DURINO KltoZKN SEASON. 



87 



SLOPE DETERMINATIONS VXD VALUES OF n IN KIT- 
TER'S FORMULA, UNDER ICE CONDITIONS. 

In 1906 two sets of slope 1 determinations and measurements of the 
other hydraulic properties were made on Connecticut River at 
Orford.N.H. 

February 17, 1906. — River in general frozen. A strip of open 
water, beginning at bridge, extended about 1,000 feet downstream. 
This was about 100 feet wide and approximately in the middle of the 
channel. The ice was rough in places and numerous ice cakes were 
frozen in, owing to high water and a partial going out of the ice during 
January. There were about 1 1 inches of snow on the ice. 

Bench marks, consisting in most cases of spikes in trees, were 
established along each bank by a double-rodded line of levels. 
Soundings for determination of cross section were made at 100 feet, 
250 feet, and 516 feet upstream from the gage. The level was set on 
the ice in the middle of the river, and water-surface elevations were 
determined on both banks at each section at holes cut in the ice. The 
following table gives results of the best set of observations : 

Slope determinations and value of'n" on Connecticut River at Orford, N. H., February 17, 

1906. 

[Gage height to water surface, 0.65 feet; gage height to bottom of ice, 5.15 feet; gage height to top of ice 
6.67 feet; discharge, 2,070 second-feet.] 



Dis- 
tance 

of sec- 
tion 

from 
gage. 


Width 

below 

ice. 


Area 

below 

ice. 


Veloc- 
ity. 


Wet- 
ted 
Per- 
imeter. 


Hy- 
draulic 

Radius. 


Dis- 
tance 

be- 
tween 

sec- 
tions. 


Differ- 
ence in 

eleva- 
tion of 

water 
surface. 


Slope. 


Aver- 
age 
Hy- 
draulic 
ra- 
dius. 


Aver- 
age 

veloc- 
ity. 


n. 


Feet. 
516 
250 
100 


Feet. 
302 
340 
329 


Sq. ft. 
2,110 
1,890 
1,730 


Ft. per 
sec. 

0.98 

1.10 

1.20 


Feet. 
605 

685 
659 


Feet. 
3.49 
2.76 
2.63 


Feet. 
266 

| 150 


Feet. 
0.026 

.043 


0.000098 
.000287 


Feet. 
3.12 

2.70 


Ft. per 
sec. 

1.04 
1.15 


0. 030 

.042 



March 15, 1906. — The conditions were about the same as during 
February, but the strips of open water were considerably shorter and 
narrower. There was no snow on the ice. Iron rods 4 or 5 feet long 
were driven into the bank to within about 6 inches of the water sur- 
face in holes cut in the ice. These were located on each bank at sec- 
tions 100 feet, 296 feet, and 516 feet upstream from the gage and the 
elevation of the tops was determined by several series of levels. 
Measurements were then made from these points to the water surface 
with a 2-foot rule. Independent observations were made at each 
point by two men, each man's set being averaged separately and the 
mean of the two sets being finally used. The results were as follows : 



88 STREAM B^LOW DURINC4 THE FROZEN SEASON. 

Slope determinations and value of'n" on Connecticut River at Orford, N. H., March 15, 1906. 

[Gage height to water surface, 5.62 feet; gage height" to bottom of iee, 4.18 feet; gage height to top of ice 
6.67 feet; discharge, 2,070 second-feet.] 



H 








C 


3 


a 

QJ 
(13 


o 
rl 


+j 




i 3 






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tn 


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XI 

"2 


o 

,Q 

03 
a) 

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> 


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03 


o 

3 
03 
u 
-a 

M 


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•° o 

QJ T3 
§8 

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M03 

03 tn 

tl 
a) 

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t> 

QJ 

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o3 

a) 
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QJ 

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c _. qj 
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QJ O 03 

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qj ^ b 
Q 


Slope. 


n. 








.F7. per 








T^i per 










Feet. 


Feet. 


Sq.ft. 


sec. 


.Feei. 


JYrf. 


.Fee/. 


.Feei. 


sec 


f 1 


Feet. 
0. 020 


0. 000091 


0.030 


516 


295 


1,800 


0.83* 


592 


3.04 


1 220 


2.67 


0.90 


ll 


.020 
.024 


. 000091 
. 000109 


.030 
.033 


296 


330 


1,530 


.98 


662 


2.31 








1 ] 


.030 


.000153 


.030 














I 196 


2. 2S 


1.01 


2 


.031 


. 000158 


.031 


100 


319 


1,440 


1.04 


640 


2.25 


! 






u 


.030 


. 000153 


.030 



Conclusions. — The mean value of n for the February obsevations is 
0.036, and for the March observations is 0.031. The March series are 
much the more reliable of the two. 



DATA FROM OTHER SOURCES. 

Up to the present time very little information has been published 
on the flow of streams under ice cover, other than that gathered by 
the United States Geological Survey. a 

Raucourt made experiments on the Neva 6 at a point where it is 900 
feet wide and of regular section, the maximum depth being 63 feet. 
When the river was frozen over the maximum velocity (2 feet 7 
inches per second) was found a little below the middle of the deepest 
vertical. It was somewhat less than double the velocity at the sur- 
face and bottom, which were nearly equal to each other. 

The United States Engineer Corps c recently made some current- 
meter measurements of flow under ice cover on St. Marys River. 

No details of the observations are given, but the general results 
were as follows: (1) The location of the threads of mean velocity was 
found to be at 0.067 and 0.753 depth. (2) The maximum velocity 
was found to be at approximately 0.4 depth. (3) The friction caused 
by the ice was found to be 0.309 of that caused by the bottom. 

Further measurements under ice cover on St. Marys River were 
made during 1905, but have not yet been reported for publication. 

Considerable data on conditions in the frozen period, duration of 
the frozen season, etc., may be found in the proceedings of the Inter- 
national Meteorological Congress, Chicago, 1893. d 

a Water-Sup. and Irr. Papers Nos. 76 (1903) and 95 (1904) . 

b Humphreys and Abbot, Physics and Hydraulics of Mississippi River, p. 190. 

c Rept. Chief of Engineers for 1897, p. 4092. 

dThe four great rivers of Siberia: Bull. U. S. Weather Bureau No. 11, 1893. 



STREAM FLOW DURING THE FROZEN 8EASON. 89 

CONCLUSIONS. 

PRACTICABILITY OF WINTER ESTIMATES OF FLOW. 

The classification of current-meter gaging stations on page ( .) indi- 
cates that about one-sixth of them remain open during the winter 
and permit about the same degree of accuracy for winter estimates 
as for those of the summer; they can, therefore, be classed with sta- 
tions south of the area subject to ice cover. About one-third of these 
stations usually have a smooth, permanent ice cover, and it is prob- 
ably fair to assume that this is about the proportion at which winter 
estimates that will be fairly reliable can be made without too great 
cost. Undoubtedly there is a further number of stations where good 
estimates can be made if sufficient attention is given by the hydrog- 
rapher, and particularly if an intelligent gage reader, with ability to 
note and sketch conditions affecting flow, is available. 

Stations at dams, in general, give less trouble during the winter 
than current-meter stations, and this should be kept in mind where 
there is any question as to which form of station is preferable. 

RECOMMENDATIONS AS TO METHODS. 

The study of the flow of streams under ice cover is but just started, 
and in order to systematize the accumulation of data and to provide 
the material in convenient form for future use it is desirable that 
certain general methods be followed. 

The methods of obtaining gage heights used should be as described 
on pages 21-23, and the observer should be especially encouraged to 
note any unusual conditions affecting flow, furnishing sketches where 
desirable. It should be kept in mind that what is desired is the 
average thickness of ice, distance from bottom of ice to water surface, 
etc., for the portion of the river near the gage, and that the hole cut 
in the ice should be so located as to give average results; preferably, 
several holes should be cut from time to time. The cost of current- 
meter measurements under ice cover can be kept within reasonable 
limits by employing laborers when necessary to cut holes in the ice, 
so as to utilize to better advantage the time of the hydrographer, and 
by using the two-point method of observations at 0.2 and 0.8 depth, 
with a few vertical velocity curves, if possible, for purposes of study. 
In case time is short a single observation at 0.5 depth will give fairly 
good results, the coefficient 0.88 being applied, or if a few vertical 
curves have been taken a closer value of the coefficient can be deter- 
mined from them. 

By following the above suggestions the total time required for a 
gaging will not be usually more than half a day, and the cost will be 
but little greater than that for a gaging under open-water conditions. 



90 STREAM FLOW DURING THE FROZEN SEASON. 

For depths less than 5 feet it is desirable to use the current meter 
fastened to a rod for convenience in handling and in order that 0.8 
depth may be reached; in fact, this method is generally preferable to 
the use of a cable where depths and velocities are not too great. 

Vertical velocity curves should be taken at typical points in the 
cross section when time permits just as for open water. These should 
always be taken just before or after the two or one point observations 
at the point in question to give further information as to the field 
accuracy of these methods, the observations by the point method not 
being incorporated in the vertical velocity curve. 

Rating curves should be constructed in each of the two ways 
described on pages 43-46, and the method which seems to give the best 
results should be used. Special efforts should be made to obtain 
gagings for thin ice cover for the purpose of better defining the rating 
curve or coefficient to use under such conditions. 

It is believed that the methods previously indicated for discharge 
measurements (pp. 22-24) will give results well within the degree of 
accuracy consistent with winter estimates of flow, and that less time 
need be spent hereafter on individual gagings. This will make it pos- 
sible to give more attention to the study and completion of station rat- 
ing curves — the direction in which the most effort should be expended 
in the immediate future. 



N DEX. 



Page 

Air. friction of 15 17,77 

Anchor ice, character of 13 

S< e also Ice. 

Barnes, II. T., on Formation of ice 11,13 

Bed, friction of, comparison of ice friction 

and 77 

Bliskirk, N. Y., gaging station at, condi- 
tions at 42 

velocity curves at. for ice cover 57 

Catskill Creek, gaging station on, condi- 
tions at 20-29, 38 

velocity curves on, for ice cover 47,73 

Catskill Mountains, streams in, measure- 
ments of 21 

Chemung, N. Y., gaging station at, condi- 
tions at 42 

needle ice at, figure showing 12 

velocity curves at, for ice cover 47, 73 

Chemung River, gaging station on, condi- 
tions at 42 

needle ice in, figure showing 12 

velocity curves on, for ice cover 47, 73 

Chippewa, Wis., gaging station at, condi- 
tions at •- 42 

Chippewa River, velocity curves on, for ice 

cover 

Climate, effect of, on ice formation 7 

Columbus, Ohio, velocity curves at, for ice 

cover 03 

Connecticut River, discharge of, relation be- 
tween ice cover and open flow in . <:o 

gaging station on, conditions at 29-30, 39 

ice on, thickness of 10 

slope determinations on 87-88 

rating curve for ice cover on 45-40 

figure showing 45 

velocity of, variations in 85-80 

velocity curves on, for ice cover. 48-51,73,74,77 

figure showing 81 

Cost of measurements under ice cover, dis- 
cussion of 24 

Current meter, measurements by, cost of. . . 24 

measurements by, methods of 22-24 

use of 90 

Current-meter stations, ice. conditions at. 9,20-38 
See also Gaging stations. 

Dams, effect of, on ice formation 8 

gaging stations at, conditions at 9 

figure showing 24 

measurements at 25 

Des Moines River, gaging station on, condi- 
tions at 42 

velocity curves on, for ice cover 51, 74 



Page. 

Discharge measurements, accuracy of 89,90 

effect <>f freezing on \<t 21 

figure showing 20 

Set also Flow; Velocity, etc. 

Droughts, periods of . r , 

Kau Claire River, gaging station on, condi- 
tions at 42 

velocity curves on, for ice cover 4S 

Esopus Creek, gaging station on, condi- 
tions at 30-32, 39 

ice on, thickness of 10 

velocity curves on, for ice cover 52 -53, 73 

Fish River, gaging station on, conditions 

at 32-33, 39 

velocity of, variations in 80 

velocity curves on, for ice cover. . . 53-54, 73, 77 

figure showing 82 

Flambeau River, gaging station on, condi- 
tions at 42 

velocity curves on, for ice cover 54 

Flow under ice, friction and, relations of. 14-17, 

19-21,77 
friction and, relations of, figures show- 
ing 20,84 

measurements of, accuracy of 89 

methods for 89-90 

See also Velocity; Discharge. 

Francis, James B., on air friction 10 

Freezing, effect of, on slope 17-18 

effect of, on slope, figure showing 17 

Freshets, winter, occurrence and character 

of 13-14 

Friction. See Air, friction of; Ice, friction 
of; Bed, friction of. 

Gaging, cost of 24,89 

methods of, in closed season 21-22,23,89 

in open season 0-7 

Gaging stations, conditions at 26-38 

discharge under ice cover at, relations 

between open section and 46 

rating curves for ice cover at 43-46 

Genesee River, gaging stations on, condi- 
tions at 42 

velocity curves on, for ice cover 55-57,73 

Hoosic River, gaging station on, conditions 

at 42 

velocity curves on, for ice cover 57 

Ice, character of 10-13 

discharge under, relation between open 

flow and 46 

flow under 14-21 

measurements of, accuracy of 89 

formation of, factors affecting 7-8 

91 



92 



INDEX. 



Page 

Ice, friction of 14-17,77 

comparison of bed friction and 77 

prevalence of 5 

roughness of, effect of, figure showing. . 84 

season of, duration of 9-10 

thickness of, change in 10 

effect of, on flow 19-21 

figure showing 20 

Kennebec River, gaging station on, condi- 
tions at 33-34, 40 

rating curve for ice cover at 44-45 

figure, showing 44 

velocity curves on, for ice cover.. . 58-61,73,77 

figure showing 79 

Keosaqua, Iowa, gaging station at, condi- 
tions at '. 42 

velocity curves at, for ice cover 54 

Kingston, N. Y., gaging station at, condi- 
tions at 30-32,39 

ice at, thickness of 10 

velocity curves at, for ice cover 52-53 

Kutler's formula, value of " n " in, under ice 

conditions 87-88 

Ladysmith, Wis., gaging station at, condi- 
tions at 42 

velocity curves at, for ice cover 54 

Madison, Me., gaging station at, view of 24 

Massena Springs, N. Y., gaging stations at, 

conditions at 42 

velocity curves at, for ice cover 64,73 

Maumee River, gaging station on, condi- 
tions at 42 

velocity curves on, for ice cover 62,74 

Middlebury, Vt., gaging station at, condi- 
tions at 42 

Minimum flow, period of 5 

Mohawk River, velocity curves on, for ice 

cover 62-63,73 

Mount Morris, N. Y., gaging stations at, 

conditions at 42 

velocity curves at, for ice cover 55,73 

Needle ice, character of 10-11 

effect of, on flow measurements 12 

formation of . . . 8 

conditions of 11 

movement in 11-12 

See also Ice. 

Neva River, velocity of, under ice 88 

Newpaltz, N. Y., gaging station at, condi- 
tions at 35-37, 40 

rating curve for ice cover at 43-44 

figure showing 43 

velocity curves at, for ice cover.. . 66-68,73,77 

figures showing 43,80 

North Anson, Me., gaging station at, condi- 
tions at 33-34, 40 

rating curve for ice cover at 44-45 

figure showing 45 

velocity curves at, for ice cover. . . 58-61, 73, 77 

figure showing 79 

Olentangy River, velocity curves on, for ice 

cover 63 

Orford, N. H., gaging station at, conditions 

at 29-30, 39 

ice at, thickness of 10 



Orford, N. H., slope determinations at 87-88 

rating curve for ice cover at 45-46 

figure showing 45 

velocity at, variations in 85-86 

velocity curves at, for ice cover... 48-51,73,77 

figure showing 81 

Otter Creek, gaging station on, conditions 

at 42 

Precipitation, flow estimates from 25-26 

Raquette River, gaging stations on, condi- 
tions at 42 

velocity curves on, for ice cover 64,73 

Rating curves, construction of 90 

details of 43-46 

Raucourt, , velocity measurements by.. 88 

Richmond, Vt., gaging station at, condi- 
tions at 37-38, 41 

gaging station at, view of 24 

velocity curves at, for ice cover... 70-71,74,77 
Rochester, N. Y., gaging stations at, condi- 
tions at 42 

velocity curves at, for ice cover 56-57, 73 

Rondout Creek, gaging station on, condi- 
tions at 34-35, 40 

velocity curves on, for ice cover . . 65,73,74,77 
Rosendale, N. Y., gaging station at, 

conditions at 34-35, 40 

velocity curves at, for ice cover 65, 73, 77 

St. Marys River, velocity of, under ice 88 

Sandy River, gaging station at, view of 24 

Sherwood, Ohio, gaging station at, condi- 
tions at 42 

velocity curves at, for ice cover 62 

Slope, determination of, under ice conditions 

17-18, 87-88 

measurement of stream flow by 7 

variation in, due to freezing 17-18 

diagram showing 17 

Snow, effect of, on formation of ice 13 

effect of, on stream flow 5, 25-26 

evaporation of 26 

South Cairo, gaging station at, conditions 

at 26-29, 38 

velocity curves at, for ice cover 47, 73 

Springs, temperature of : 8 

Stearns, F. P., on form of vertical velocity 

curves 75-76 

Streams, character of, effect of, on ice form- 
ation 7,8 

flow of. See Flow; Disharge: Velocity; 
etc. 

Surface ice, character of 11 

See also Ice. 
Twin Rock Bridge, .N. Y., gaging station at, 

conditions at 42 

velocity curves at, for ice cover.... 69,74 

Utica, N. Y., velocity curves at, for ice 

cover 62-63, 73 

Velocities, mean and 0.2 and 0.8 depth, re- 
lations of 83-85 

Velocities, mid depth and mean, relations of .82-83 
Velocity, measurement of stream flow by. . 6-7 

position of maximum thread of 81-82 

position of mean thread of 79-81 

observations on, accuracy of 89 

variation in, at different depths 85-86 



INDEX. 



93 



Pag 
Vertical velocity curves for ice cover, Change 

of, with change of stage so 

change of, figures showing 79,81 

comparison of curves withoul Ice cover 

and 7s 79 

Dgure showing 78 

depth and relations of,-flgure showing. 83 

detailsof W 73 

form of 75 77 

figures showing . . . 75, 78, 79, 80, 81 . 82, 83,84 
relation of depth and velocity to... 

rough Ice, and relations of, figure 

showing 84 

summaries of 72 71 

Wallagrass, Me., gaging station at, condi- 
tions at 32-33,39 

velocity at, variations in 86 

velocity curvesat, foricecovcr 53-54,73,77 

figure showing 82 

Wallkill River, discharge of, relation be- 
tween ice rover and open water 

at 46 

gaging station on, conditions at 35-37,40 

rating curve for ieo cover at 43-44 



Page. 

Wallkill River, gaging station on, rating 

curve for icecover at, figure showing 13 

velocity curves on, for ice cover 66-68, 

73,74, 77,78 

figures showing 13 BO 

Waterway, area of, change in, due to free/ 

ing 18 

Weirs, measurement of stream Mow by.... 6 
West Canada Creek, gaging station on. con 

ditions at 42 

velocity curves on. for ice cover 69,74 

W'inooski River, gaging station on, condi 

tions at .'(7 :is. 11 

gaging stat ion on, view of 2 1 

velocity curves on, for ice cover 70-71,74,77 

Winter, conditions during 7-14 

conditions during, classification of . ... 8-9 

observations during, accuracy of 89 

See also Ice. 

Winter records, accuracy of 89 

discussion of 26-87 

importance of 5 

methods of obtaining 21-26 

See aiso Gaging. 



CLASSIFICATION OF THE PUBLICATIONS OF THK UNITKD STATES GEOLOGICAL 

SURVEY. 

[Water-Supply Paper No. 187.] 

The serial publications of the United States ( reological Survey consist <>f ( 1 ) Annual 
Reports, (2) Monographs, (3) Professional Papers, (4) Bulletins, (5) Mineral 
Resources, (6) Water-Supply and Irrigation Papers, (7) Topographic Atlas of United 
States — folios and separate sheets thereof, (8) Geologic Atlas of the United States — 
folios thereof. The classes numbered 2, 7, and 8 are sold at cost of publication; the 
others are distributed free. A circular giving complete, lists can be had on application. 

Most of the above publications can be obtained or consulted in the following ways: 

1. A limited number are delivered to the Director of the Survey, from whom they 
can be obtained, free of charge (except classes 2, 7, and 8), on application. 

2. A certain number are delivered to Senators and Representatives in Congress 
for distribution. 

3. Other copies are deposited with the Superintendent of Documents, Washington, 
D. C, from whom they can be had at prices slightly above cost. 

4. Copies of all Government publications are furnished to the principal public 
libraries in the large cities throughout the United States, where they can be con- 
sulted by those interested. 

The Professional Papers, Bulletins, and Water-Supply Papers treat of a variety of 
subjects, and the total number issued is large. They have therefore been classified 
into the following series: A, Economic geology; B, Descriptive geology; C, System- 
atic geology and paleontology; D, Petrography and mineralogy; E, Chemistry and 
physics; F, Geography; G, Miscellaneous; H, Forestry; I, Irrigation; J, Water stor- 
age; K, Pumping water; L, Quality of water; M, General hydrographic investiga- 
tions; N, Water power; O, Underground waters; P, Hydrographic progress reports. 
This paper is the nineteenth in Series M, the complete list of which follows 
(WS=Water-Supply Paper): 

Series M — General Hydrographic Investigations. 

WS 56. Methods of stream measurement. 1901. 51 pp., 12 pis. 

WS 64. Accuracy of stream measurements, by E. C. Murphy. 1902. 99 pp., 4 pis. 

WS 76. Observations on the flow of rivers in the vicinity of New York City, by H. A. Pressey. 1902. 

108 pp., 13 pis. 
WS 80. The relation of rainfall to run-off, by G. W. Rafter. 1903. 104 pp. 
WS 81. California hydrography, by J. B. Lippincott. 1903. 488 pp., 1 pi. 
WS ss. The Passaic flood of 1902, by G. B. Hollister and M. O. Leighton. 1903. 56 pp., 15 pis. 
WS 91. Natural features and economic development of the Sandusky, Maumee, Muskingum, and 

Miami drainage areas in Ohio, by B. H. Flynn and M. S. Flynn. 1904. 130 pp. 
WS 92. The Passaic flood of 1903, by M. O. Leighton. 1904. 48 pp., 7 pis. 
WS 94. Hydrographic manual of the United States Geological Survey, prepared by E. C. Murphy, 

J. C. Hoyt, and G. B. Hollister. 1904. 76 pp., 3 pis. 
WS 95. Accuracy of stream measurements CseconiT edition), by E. C. Murphy. 1904. 169 pp., 6 pis. 
WS 96. Destructive floods in the United States in 1903, by E. C. Murphy. 1904. 81 pp., 13 pis. 
WS 106. Water resources of the Philadelphia district, by Florence Bascom. 1904. 75 pp., 4 pis. 
WS 109. Hydrograpny of the Susquehanna River drainage basin, by J.C. Hoyt and R. H.Anderson. 

1904. 215 pp., 28 pis. 

I 



II SERIES LIST. 

WS 116. Water resources near Santa Barbara, California, by J. B. Lippincott. 1904. 99 pp., 8 pis. 
WS 147. Destructive floods in the United States in 1904, by E. C. Murphy and others. 1905. 206 pp., 

18 pis. 
WS 150. Weir experiments, coefficients, and formulas, by R. E. Horton. 1906. 189 pp., 38 pis. 
WS 162. Destructive floods in the United States in 1905, by E. C. Murphy and others. 1906. 105 pp., 

4 pis. 
WS 180. Turbine water-wheel tests and power tables, by Robert E. Horton. 1906. 134 pp., 2 pis. (Out 

of stock.) 
WS 187. Determination of stream flow during the frozen season, by H. K. Barrows and Robert E. 

Horton. 1907. 93 pp., 1 pi. 

Correspondence should be addressed to 

The Director, 

United States Geological Survey, 

Washington, D. C. 
December, 1906. 

o 



lr'08 



LIBRARY OF CONGRESS 



019 953 636 9 




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